A347887 Odd numbers k for which A003415(sigma(k^2))-(k^2) is strictly positive and even. Here A003415 is the arithmetic derivative.

201, 231, 237, 259, 273, 315, 333, 399, 429, 455, 483, 525, 555, 585, 627, 651, 665, 741, 763, 855, 903, 975, 1057, 1071, 1085, 1113, 1209, 1235, 1351, 1395, 1407, 1505, 1533, 1635, 1659, 1677, 1767, 1785, 1935, 2037, 2079, 2163, 2211, 2265, 2317, 2331, 2345, 2451, 2457, 2479, 2541, 2555, 2583, 2607, 2611, 2613

Offset: 1

Author

Antti Karttunen, Sep 19 2021

Keywords

• nonn

Comments

A square root of any hypothetical odd term x in A005820 (triperfect numbers) would be a member of this sequence, because such x should be a term of A342923 [Numbers x such that A342925(x)-x = 3*A003415(x)], and as the right hand side would then certainly be even (A235992 contains all odd squares), the left hand side should also be even. See also comments in A347870 and in A347391.

Crossrefs

Cf. A000203, A003415, A005820, A097023, A235991, A235992, A342923, A342925, A342926, A347383, A347391.

Subsequence of A347881 and of A347885. The intersection with A347882 gives A347888.

Programs

Mathematica

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 3000, 2], (d = ad[DivisorSigma[1, #^2]] - #^2) > 0 && EvenQ[d] &] (* 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]));
isA347887(n) = if(!(n%2),0,my(u=(A003415(sigma(n^2))-(n^2))); ((u>0)&&!(u%2)));