A029715 a(n) = Sum_{k divides 2^n} S(k), where S is the Kempner function A002034.

1, 3, 7, 11, 17, 25, 33, 41, 51, 63, 75, 89, 105, 121, 137, 153, 171, 191, 211, 233, 257, 281, 305, 331, 359, 387, 417, 449, 481, 513, 545, 577, 611, 647, 683, 721, 761, 801, 841, 883, 927, 971, 1017, 1065, 1113, 1161, 1209, 1259, 1311, 1363, 1417, 1473, 1529

Offset

0,2

Links

Table of n, a(n) for n=0..52.

Maple

A002034 := proc(n) local m; m :=1 ; while type(factorial(m)/n, 'integer') = false do m := m+1 ; od ; RETURN(m) ; end: A029715 := proc(n) local a, i; a :=0 ; for i from 0 to n do a := a+A002034(2^i) ; od ; RETURN(a) ; end: for n from 0 to 80 do printf("%d, ", A029715(n)) ; od ; # R. J. Mathar, Jun 06 2007

Mathematica

S[n_] := S[n] = Module[{k = 1}, While[True, If[Divisible[k!, n], Return[k], k++]]];
a[n_] := S /@ Divisors[2^n] // Total;
a /@ Range[0, 52] (* Jean-François Alcover, Nov 17 2020 *)

Crossrefs

Cf. A029714, A002034.

Sequence in context: A180452 A294479 A331968 * A088803 A350146 A194069

Adjacent sequences: A029712 A029713 A029714 * A029716 A029717 A029718

Keyword

nonn

Author

Norbert Hungerbuhler (buhler(AT)math.ethz.ch)

Extensions

More terms from R. J. Mathar, Jun 06 2007

Status

approved