A347891 Odd numbers k such that sigma(k^2) > 2*k^2 and A003415(sigma(k^2)) < k^2.

495, 735, 945, 1485, 1755, 2205, 2475, 2625, 2805, 3315, 3675, 3795, 4455, 4785, 4845, 5145, 5265, 5445, 6615, 6765, 7425, 7605, 7755, 8085, 8415, 8505, 8745, 8775, 9735, 11025, 12375, 12495, 13365, 13965, 14025, 15435, 15795, 16065, 16335, 16905, 17595, 18375, 19845, 20295, 21315, 22185, 22275, 22785, 22815, 23265

Offset: 1

Author

Antti Karttunen, Sep 19 2021

Keywords

• nonn

Comments

Odd numbers whose square is abundant and present in A343216.

The first term that is not a multiple of 5 is a(146) = 82467.

Links

• Index entries for sequences related to sigma(n)

Crossrefs

Square roots of A347890. Subsequence of A174830.

Cf. A000196, A000203, A003415, A005231, A343216.

Programs

Mathematica

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 24000, 2], DivisorSigma[1, #^2] > 2*#^2 && ad[DivisorSigma[1, #^2]] < #^2 &] (* Amiram Eldar, Sep 19 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA347891(n) = if(!(n%2),0,my(u=n*n); (A003415(sigma(u))(2*u)));

Formula

a(n) = A000196(A347890(n)).