A319713 Sum of A276150(d) over proper divisors d of n, where A276150 gives the sum of digits in primorial base.

0, 1, 1, 2, 1, 4, 1, 4, 3, 5, 1, 7, 1, 4, 6, 6, 1, 8, 1, 10, 5, 6, 1, 11, 4, 5, 6, 9, 1, 15, 1, 10, 7, 7, 6, 15, 1, 6, 6, 16, 1, 15, 1, 13, 13, 8, 1, 19, 3, 13, 8, 12, 1, 17, 8, 17, 7, 9, 1, 24, 1, 4, 13, 12, 7, 17, 1, 12, 9, 17, 1, 23, 1, 5, 15, 11, 7, 17, 1, 24, 12, 7, 1, 28, 9, 6, 10, 19, 1, 27, 6, 15, 5, 8, 8, 25, 1, 12, 13, 24, 1, 19, 1, 20, 21

Offset: 1

Author

Antti Karttunen, Oct 02 2018

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A276150, A319711, A319715.

Programs

Mathematica

d[n_] := Module[{k = n, p = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, s += r; p = NextPrime[p]]; s]; a[n_] := DivisorSum[n, d[#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Mar 05 2024 *)

PARI

A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
A319713(n) = sumdiv(n,d,(dA276150(d));

Formula

a(n) = Sum_{d|n, dA276150(d).

a(n) = A319715(n) - A276150(n).