35 (number)

{{Infobox number

| number = 35

| divisor = 1, 5, 7, 35

}}

35 (thirty-five) is the natural number following 34 and preceding 36.

In mathematics

Image:Pyramid of 35 spheres animation.gif

35 is the sum of the first five triangular numbers, making it a tetrahedral number.{{Cite web|url=https://oeis.org/A000292|title=Sloane's A000292 : Tetrahedral numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-31}}

35 is the 10th discrete semiprime ( $5 \times 7$ ){{Cite OEIS|sequencenumber=A001358}} and the first with 5 as the lowest non-unitary factor, thus being the first of the form (5.q) where q is a higher prime.

35 has two prime factors, (5 and 7) which also form its main factor pair (5 x 7) and comprise the second twin-prime distinct semiprime pair.

The aliquot sum of 35 is 13, within an aliquot sequence of only one composite number (35,13,1,0) to the Prime in the 13-aliquot tree. 35 is the second composite number with the aliquot sum 13; the first being the cube 27.

35 is the last member of the first triple cluster of semiprimes 33, 34, 35. The second such triple distinct semiprime cluster is 85, 86, and 87.{{Cite OEIS|sequencenumber=A001748}}

35 is the number of ways that three things can be selected from a set of seven unique things, also known as the "combination of seven things taken three at a time".

35 is a centered cube number,{{Cite web|url=https://oeis.org/A005898|title=Sloane's A005898 : Centered cube numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-31}} a centered tetrahedral number, a pentagonal number,{{Cite web|url=https://oeis.org/A000326|title=Sloane's A000326 : Pentagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-31}} and a pentatope number.{{Cite web|url=https://oeis.org/A000332|title=Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-31}}

35 is a highly cototient number, since there are more solutions to the equation $x - \varphi (x) = 35$ than there are for any other integers below it except 1.{{Cite web|url=https://oeis.org/A100827|title=Sloane's A100827 : Highly cototient numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-31}}

There are 35 free hexominoes, the polyominoes made from six squares.

Since the greatest prime factor of $35^{2} + 1 = 1226$ is 613, which is more than 35 twice, 35 is a Størmer number.{{Cite web|url=https://oeis.org/A005528|title=Sloane's A005528 : Størmer numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-31}}

35 is the highest number one can count to on one's fingers using senary.

35 is the number of quasigroups of order 4.

35 is the smallest composite number of the form $6k+5$ , where {{Mvar|k}} is a non-negative integer.

References

Category:Integers