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

Author

Antti Karttunen, Sep 18 2021

Keywords

• nonn

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)

Crossrefs

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

Subsequence of A347881. The intersection with A347887 gives A347888.

Cf. also A342923.

Programs

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 *)

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)));