A353456 Numbers k such that A353627(k) is less than A353628(k).

81, 162, 243, 324, 405, 486, 567, 625, 648, 810, 891, 972, 1053, 1134, 1215, 1250, 1296, 1377, 1539, 1620, 1701, 1782, 1863, 1875, 1944, 2106, 2268, 2349, 2401, 2430, 2500, 2511, 2592, 2673, 2754, 2835, 2997, 3078, 3125, 3159, 3240, 3321, 3402, 3483, 3564, 3726, 3750, 3807, 3888, 4131, 4212, 4293, 4375, 4455, 4536

Offset

1,1

Comments

Numbers in A353511 but not in A122132. Positions where A353627 and A353628 differ from each other. See discussion in A209635.

a(8) = 625 is the first term that is not a multiple of 81.

If k is present in the sequence, then 2*k and A000265(k) are present also.

Links

Table of n, a(n) for n=1..55.

Prog

(PARI)
A001001(n) = sumdivmult(n, d, sigma(d)*d); \\ From A001001
A353628(n) = (A001001(n)%2);
A353627(n) = issquarefree(n>>valuation(n, 2));
isA353456(n) = (A353627(n) != A353628(n));
(PARI) isA353456(n) = if(issquarefree(n=(n>>valuation(n, 2))), 0, my(f=factor(n)); for(k=1, #f~, if((f[k, 2]%4)>1, return(0))); (1)); \\ After Álvar Ibeas's Nov 28 2017 comment in A209635

Crossrefs

Setwise difference A353511 \ A122132. Subsequence of A038838.

Cf. A000265, A001001, A209635, A353627, A353628.

Sequence in context: A206065 A139705 A226643 * A044251 A043454 A044632

Adjacent sequences: A353453 A353454 A353455 * A353457 A353458 A353459

Keyword

nonn

Author

Antti Karttunen, May 03 2022

Status

approved