A342921 a(n) = A003415(A019565(n)).

0, 1, 1, 5, 1, 7, 8, 31, 1, 9, 10, 41, 12, 59, 71, 247, 1, 13, 14, 61, 16, 87, 103, 371, 18, 113, 131, 493, 167, 719, 886, 2927, 1, 15, 16, 71, 18, 101, 119, 433, 20, 131, 151, 575, 191, 837, 1028, 3421, 24, 191, 215, 859, 263, 1241, 1504, 5153, 311, 1623, 1934, 6871, 2556, 10117, 12673, 40361, 1, 19, 20, 91, 22, 129

Offset: 0

Author

Antti Karttunen, Apr 06 2021

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A003415, A019565, A069359, A276156, A327860, A329029, A342002.

Programs

Mathematica

Array[If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &[Times @@ Prime@ Flatten@ Position[Reverse@ IntegerDigits[#, 2], 1]] &, 70, 0] (* Michael De Vlieger, Apr 08 2021 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A342921(n) = A003415(A019565(n));

Formula

a(n) = A003415(A019565(n)) = A069359(A019565(n)).

a(n) = A327860(A276156(n)) = A329029(A276156(n)) = A342002(A276156(n)).