A387418 Numbers k such that the odd part of (1+k) divides (1 + odd part of A034448(k)), where A034448 is unitary sigma (usigma).

1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 1791, 2047, 2431, 4095, 8191, 14335, 14847, 16383, 27391, 32767, 44031, 57855, 65535, 114687, 131071, 204799, 262143, 376831, 524287, 923647, 1048575, 1632255, 2056191, 2097151, 2744319, 4194303, 6815743, 8388607, 8781823, 8978431, 12058623, 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..44.

Prog

(PARI)
A000265(n) = (n>>valuation(n, 2));
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); };
isA387418(n) = !((1+A000265(A034448(n)))%A000265(1+n));

Crossrefs

Cf. A000225 (subsequence), A000265, A002827, A004767, A034448.

For similar sequences, see A336700, A387410, A387415, A387419.

Sequence in context: A043755 A105755 A043764 * A213248 A336700 A387415

Adjacent sequences: A387415 A387416 A387417 * A387419 A387420 A387421

Keyword

nonn

Author

Antti Karttunen, Sep 01 2025

Status

approved