

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.


2



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
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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



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

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


KEYWORD

nonn


AUTHOR



STATUS

approved



