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

1,2

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.

Links

Table of n, a(n) for n=1..45.

Prog

(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));

Crossrefs

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

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

Sequence in context: A267258 A305493 A213247 * A043755 A105755 A043764

Adjacent sequences: A387407 A387408 A387409 * A387411 A387412 A387413

Keyword

nonn

Author

Antti Karttunen, Sep 01 2025

Status

approved