A347881 Odd numbers k for which A003415(sigma(k^2)) > k^2, where A003415 is the arithmetic derivative.

105, 201, 231, 237, 259, 273, 315, 333, 399, 429, 455, 469, 483, 525, 553, 555, 585, 603, 627, 651, 665, 693, 711, 741, 763, 777, 819, 855, 871, 903, 975, 1001, 1005, 1027, 1057, 1071, 1085, 1113, 1119, 1141, 1155, 1185, 1197, 1209, 1221, 1235, 1273, 1281, 1287, 1295, 1351, 1365, 1395, 1407, 1443, 1449, 1463, 1467, 1501

Offset: 1

Author

Antti Karttunen, Sep 18 2021

Keywords

• nonn

Comments

Odd numbers k such that A342926(k^2) is strictly positive.

Square roots of odd squares present in A343218.

Crossrefs

Cf. A000203, A003415, A343218, A342926, A347882 (subsequence).

Programs

Mathematica

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 1501, 2], ad[DivisorSigma[1, #^2]] > #^2 &] (* Amiram Eldar, Sep 18 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA347881(n) = ((n%2)&&(A003415(sigma(n^2))>(n^2)));