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

1,1

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

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 *)

Prog

(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));

Crossrefs

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

Intersection of A347872 and A351562.

Sequence in context: A044377 A044758 A053743 * A386429 A234336 A173371

Adjacent sequences: A347871 A347872 A347873 * A347875 A347876 A347877

Keyword

nonn

Author

Antti Karttunen, Sep 18 2021

Status

approved