A347882 Odd numbers k for which A003415(sigma(k^2))-(k^2) is strictly positive and a multiple of 3. Here A003415 is the arithmetic derivative.

273, 399, 651, 741, 777, 819, 903, 1197, 1209, 1281, 1365, 1407, 1443, 1533, 1659, 1677, 1767, 1925, 1953, 1995, 2035, 2037, 2109, 2163, 2223, 2289, 2331, 2379, 2451, 2457, 2613, 2667, 2709, 2847, 2919, 3003, 3081, 3171, 3255, 3297, 3423, 3441, 3477, 3591, 3627, 3685, 3705, 3783, 3801, 3819, 3843, 3885, 3999, 4017

Offset

1,1

Comments

Of the first 200 terms of A097023, 44 appear also in this sequence, the first ones being 50281, 73535, 379953, etc. The square root of any hypothetical odd term appearing in A005820 should satisfy both conditions, and the term itself should appear in both A347383 and A347391.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sigma(n)

Mathematica

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 4000, 2], (d = ad[DivisorSigma[1, #^2]] - #^2) > 0 && Divisible[d, 3] &] (* Amiram Eldar, Sep 18 2021 *)

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA347882(n) = if(!(n%2), 0, my(u=(A003415(sigma(n^2))-(n^2))); ((u>0)&&!(u%3)));

Crossrefs

Cf. A000203, A003415, A005820, A097023, A342925, A342926, A347383, A347391.

Subsequence of A347881. The intersection with A347887 gives A347888.

Cf. also A342923.

Sequence in context: A217004 A256638 A338557 * A347888 A306812 A157374

Adjacent sequences: A347879 A347880 A347881 * A347883 A347884 A347885

Keyword

nonn

Author

Antti Karttunen, Sep 18 2021

Status

approved