A319712 - OEIS

A319712

Sum of A034968(d) over divisors d of n, where A034968 gives the sum of digits in factorial base.

1, 2, 3, 4, 4, 5, 3, 6, 6, 8, 5, 9, 4, 7, 10, 10, 6, 11, 5, 14, 10, 11, 7, 12, 6, 7, 9, 12, 5, 17, 4, 13, 11, 11, 11, 18, 5, 10, 11, 21, 7, 19, 6, 18, 19, 14, 8, 18, 6, 13, 12, 13, 6, 17, 12, 18, 12, 11, 7, 29, 6, 10, 19, 19, 14, 23, 7, 19, 16, 25, 9, 24, 5, 10, 17, 17, 13, 19, 6, 30, 15, 14, 8, 31, 15, 13, 14, 27, 9, 35, 13, 23, 14, 17, 17

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OFFSET

1,2

COMMENTS

Inverse Möbius transform of A034968.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..40320

Index entries for sequences related to factorial base representation.

FORMULA

a(n) = Sum_{d|n} A034968(d).

a(n) = A319711(n) + A034968(n).

MATHEMATICA

d[n_] := Module[{k = n, m = 2, s = 0, r}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, s += r; m++]; s]; a[n_] := DivisorSum[n, d[#] &]; Array[a, 100] (* Amiram Eldar, Feb 14 2024 *)

PROG

(PARI)

A034968(n) = { my(s=0, b=2, d); while(n, d = (n%b); s += d; n = (n-d)/b; b++); (s); };

A319712(n) = sumdiv(n, d, A034968(d));

CROSSREFS

Cf. A034968, A319711, A319715.

Sequence in context: A058277 A065852 A303998 * A319715 A088807 A036371

Adjacent sequences: A319709 A319710 A319711 * A319713 A319714 A319715

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Oct 02 2018

STATUS

approved