Talk:Unitary perfect number

N = p1^a1 * p2^a2 * p3^a3 * p4^a4 * ... * pn^an

i = 1, 2, 3, 4, ..., n

If ai = 3, take in the product the sum of pi^3 + pi^2 + pi + 1.

If ai = 6, take in the product the sum of pi^6 + pi^4 + pi^2 + 1.

If ai = any number other than 3 or 6 = n (say), take in the product the sum of pi^n + 1.

All known unitary multiply perfect numbers, except 87360, is tri-unitary multiply perfect for same k because only 87360 has a prime factor with power 3 or 6, here, it has power 6 on 2. All multiply perfect numbers with only powers 1 and 3 on their prime factors are tri-unitary multiply perfect for same k, including 6 = 2 * 3 and 120 = 2^3 * 3 * 5. 2409:40E0:11BD:90E3:50BB:7842:A452:E409 (talk) 10:33, 24 January 2025 (UTC)