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

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to primorial base.

Formula

a(n) = Sum_{d|n, d<n} A276150(d).

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

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 *)

Prog

(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, (d<n)*A276150(d));

Crossrefs

Cf. A276150, A319711, A319715.

Sequence in context: A112350 A321437 A319711 * A063717 A024994 A243329

Adjacent sequences: A319710 A319711 A319712 * A319714 A319715 A319716

Keyword

nonn,base

Author

Antti Karttunen, Oct 02 2018

Status

approved