cp's OEIS Frontend

Number of terms <10^n: 0, 0, 0, 0, 2, 7, 24, 83, 250, 792, 2484, 7988, 25383, 80082, ..., . Not all are a multiple of 25, i.e.; 81162081 = 9009^2 = (9*7*11*13)^2. See A156943.

Any term must be an odd square. Square roots are in A174830.

Indeed, the sum of divisors of any number isn't odd unless it's a square or twice a square (A028982), and to get the abundance, twice the number is subtracted, so the parity remains the same. - M. F. Hasler, Jan 26 2020

Question: Is this a subsequence of A379503? (Is A379504(a(n)) > 0 for all n? See A379951). The first 15000 terms are all included there. - Amiram Eldar and Antti Karttunen, Jan 06 2025

Question 2: Is A379505(a(n)) > 1 for all n, especially if there are no quasiperfect numbers (numbers k such that sigma(k) = 2k+1)? - Antti Karttunen, Jan 06 2025

From Amiram Eldar, Jan 16 2025: (Start)

The least term that is not divisible by 5 is a(75) = 81162081.

The least term that is not divisible by 3 is a(296889) = 1382511906801025.

The least term that is coprime to 15 is 15285071557677427358507559514565648611799881. (End)

Question: Does A379504(.) obtain generally smaller values for the terms of this subsequence of A156942 than for its non-primitive terms? (See A379951, with A379951(5) = 5969, where A156942(5) = 342225, the first term of this sequence). Is A103977(.) = 1 for all terms, i.e., is this a subsequence of A379503?