A347874 Odd composites for which A342926(n) is even and A342926(2*n) is a multiple of 3.

45, 153, 261, 325, 369, 405, 441, 477, 801, 909, 925, 1017, 1233, 1341, 1377, 1521, 1525, 1557, 1573, 1773, 1825, 2097, 2205, 2313, 2349, 2401, 2421, 2425, 2529, 2637, 2725, 2853, 3177, 3249, 3321, 3501, 3609, 3645, 3757, 3825, 3925, 4041, 4149, 4293, 4477, 4525, 4581, 4689, 4825, 5013, 5121, 5337, 5445, 5553, 5725

Offset: 1

Author

Antti Karttunen, Sep 18 2021

Keywords

• nonn
• changed

Comments

Numbers k for which A347871(k) = 0 and A347883(2*k) = 0.

This is not a subsequence of A228058. The terms that do not occur there: 441, 1521, 2401, 3249, 8649, 16641, 28561, 35721, etc., seem all to be squares. Terms of A228058 missing from this sequence are: 117, 245, 333, 425, 549, 605, 637, 657, 725, etc. (See A351574.) Terms that are also in A228058 are given in A386429.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences where odd perfect numbers must occur, if they exist at all

Crossrefs

Cf. A000203, A003415, A228058, A342925, A342926, A347871, A347883, A351574, A386429 (subsequence).

Intersection of A347872 and A351562.

Programs

Mathematica

ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); f[n_] := ad[DivisorSigma[1, n]] - n; Select[Range[1, 5725, 2], CompositeQ[#] && EvenQ[f[#]] && Divisible[f[2*#], 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]));
A342926(n) = (A003415(sigma(n))-n);
isA347874(n) = ((n%2)&&!isprime(n)&&!(A342926(n)%2)&&!(A342926(2*n)%3));