A387410 Numbers k such that the odd part of (1+k) divides (1 + odd part of A048250(k)), where A048250 is sum of the squarefree divisors of n.

1, 3, 7, 15, 31, 63, 127, 255, 511, 639, 1023, 2047, 2431, 4095, 5247, 8191, 14335, 16383, 32767, 40959, 44031, 57855, 65535, 90111, 126975, 131071, 204799, 229375, 262143, 376831, 524287, 923647, 1048575, 1632255, 2056191, 2097151, 2621439, 2744319, 4194303, 6815743, 8388607, 8781823, 16777215, 19922943, 24068095

Offset: 1

Author

Antti Karttunen, Sep 01 2025

Keywords

• nonn
• new

Comments

Like in many sequences of this type, the criterion seems to strongly select for numbers with a long tail of trailing 1-bits. The initial 1 is probably the only term that is not in A004767.

Crossrefs

Cf. A000225 (subsequence), A000265, A004767, A048250.

For similar sequences, see A336700, A387411, A387415, A387418, A387419.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
isA387410(n) = !((1+A000265(A048250(n)))%A000265(1+n));