A387419 Numbers k such that the odd part of (1+k) divides (1 + odd part of A003959(k)), where A003959 is multiplicative with a(p^e) = (p+1)^e.

1, 3, 4, 7, 15, 31, 40, 63, 127, 255, 511, 639, 1023, 2047, 2175, 2431, 4095, 5247, 8191, 14335, 16383, 32767, 40959, 44031, 57855, 65535, 90111, 131071, 204799, 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. Terms 1, 4 and 40 are probably the only terms that are not in A004767.

Crossrefs

Cf. A000225 (subsequence), A000265, A003959, A004767.

For similar sequences, see A336700, A387410, A387411, A387415, A387418.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
isA387419(n) = !((1+A000265(A003959(n)))%A000265(1+n));