A387415 Numbers k such that the odd part of (1+k) divides (1 + odd part of A001615(k)), where A001615 is Dedekind's psi-function.

1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 2431, 4095, 8191, 14335, 16383, 27135, 32767, 44031, 57855, 65535, 75775, 131071, 204799, 262143, 376831, 524287, 667135, 923647, 1048575, 1441791, 1632255, 2056191, 2097151, 2315775, 2744319, 4194303, 6768639, 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, A001615.

For similar sequences, see A336700, A387410, A387418, A387419.

Programs

PARI

A000265(n) = (n>>valuation(n,2));
A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));
isA387415(n) = !((1+A000265(A001615(n)))%A000265(1+n));