A347888 Odd numbers k for which A003415(sigma(k^2))-(k^2) is strictly positive and a multiple of six. Here A003415 is the arithmetic derivative.

273, 399, 651, 741, 903, 1209, 1407, 1533, 1659, 1677, 1767, 2037, 2163, 2331, 2451, 2457, 2613, 2667, 2847, 3003, 3081, 3297, 3423, 3591, 3685, 3783, 3819, 3843, 3885, 3999, 4017, 4095, 4161, 4179, 4329, 4345, 4389, 4431, 4503, 4683, 4953, 5061, 5187, 5529, 5691, 5817, 5859, 5871, 5985, 6123, 6231, 6279, 6327, 6357

Offset

1,1

Comments

A square root of any hypothetical odd term x (if such numbers exist) in A005820 (triperfect numbers) should be a member of this sequence. See comments in A347882, A347887 and also in A347870 and in A347391.

Of the first 200 terms of A097023, 44 appear also in this sequence, the first ones being 50281, 73535, 379953, etc.

Links

Table of n, a(n) for n=1..54.

Mathematica

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 6500, 2], (d = ad[DivisorSigma[1, #^2]] - #^2) > 0 && Divisible[d, 6] &] (* 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]));
isA347888(n) = if(!(n%2), 0, my(u=(A003415(sigma(n^2))-(n^2))); ((u>0)&&!(u%6)));

Crossrefs

Intersection of A347882 and A347887. Subsequence of A347881 and of A347885.

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

Sequence in context: A256638 A338557 A347882 * A306812 A157374 A043467

Adjacent sequences: A347885 A347886 A347887 * A347889 A347890 A347891

Keyword

nonn

Author

Antti Karttunen, Sep 19 2021

Status

approved