A319715 Sum of A276150(d) over divisors d of n, where A276150 gives the sum of digits in primorial base.

1, 2, 3, 4, 4, 5, 3, 6, 6, 8, 5, 9, 4, 7, 10, 10, 6, 11, 5, 14, 10, 11, 7, 15, 9, 10, 12, 15, 8, 16, 3, 12, 10, 10, 10, 17, 4, 9, 10, 20, 6, 18, 5, 17, 18, 13, 7, 23, 8, 18, 14, 18, 8, 22, 14, 23, 14, 16, 9, 26, 4, 7, 17, 16, 12, 20, 5, 16, 14, 22, 7, 27, 6, 10, 21, 17, 14, 22, 7, 30, 19, 14, 9, 34, 16, 13, 18, 27, 10, 30, 10, 19, 10

Offset

1,2

Comments

Inverse Möbius transform of A276150.

Links

Antti Karttunen, Table of n, a(n) for n = 1..30030

Index entries for sequences related to primorial base.

Formula

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

a(n) = A319713(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[#] &]; 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); };
A319715(n) = sumdiv(n, d, A276150(d));

Crossrefs

Cf. A276150, A319712, A319713.

Sequence in context: A065852 A303998 A319712 * A088807 A036371 A036370

Adjacent sequences: A319712 A319713 A319714 * A319716 A319717 A319718

Keyword

nonn,base

Author

Antti Karttunen, Oct 02 2018

Status

approved