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

1,1

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.

Links

Table of n, a(n) for n=1..56.

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 *)

Prog

(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)));

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.

Sequence in context: A107843 A296022 A338591 * A353081 A259768 A076192

Adjacent sequences: A347884 A347885 A347886 * A347888 A347889 A347890

Keyword

nonn

Author

Antti Karttunen, Sep 19 2021

Status

approved