A379949 Primitive abundant numbers (A091191) that are odd squares.

342225, 1029447225, 1757705625, 2177622225, 14787776025, 18114198921, 32871503025, 45018230625, 150897287025, 245485566225, 296006724225, 705373218225, 1126920249225, 1329226832241, 1358425215225, 1545732725625, 1555265892609, 1783322538921, 2811755495241, 4627123655625, 5248080775161, 6140855705625, 7683069267225

Offset: 1

Author

Antti Karttunen, Jan 07 2025

Keywords

• nonn

Comments

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?

Links

• Amiram Eldar, Table of n, a(n) for n = 1..3500 (terms 1..725 from Antti Karttunen)

Crossrefs

Cf. A103977, A379504, A379950 (square roots).

Intersection of A016754 and A091191.

Intersection of A006038 and A156942.

Subsequences of the following sequences: A306796 (odd terms, but only if there are no odd perfect numbers), A363176, A379503 (conjectured).

Programs

PARI

is_A379949(n) = if(!(n%2) || !issquare(n) || sigma(n)<=2*n, 0, fordiv(n, d, if(d>1 && sigma(n/d, -1)>2, return(0))); (1));

PARI

is1(k) = {my(f = factor(k)); for(i = 1, #f~, f[i, 2] *= 2); if(sigma(f, -1) <= 2, return(0)); for(i = 1, #f~, f[i, 2] -= 1; if(sigma(f, -1) > 2, return(0)); f[i, 2] += 1); 1;}
list(lim) = forstep(k = 1, lim, 2, if(is1(k), print1(k^2, ", "))); \\ Amiram Eldar, Mar 12 2025

Formula

a(n) = A379950(n)^2.