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%I #14 Nov 17 2020 08:25:14
%S 1,3,7,11,17,25,33,41,51,63,75,89,105,121,137,153,171,191,211,233,257,
%T 281,305,331,359,387,417,449,481,513,545,577,611,647,683,721,761,801,
%U 841,883,927,971,1017,1065,1113,1161,1209,1259,1311,1363,1417,1473,1529
%N a(n) = Sum_{k divides 2^n} S(k), where S is the Kempner function A002034.
%p 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
%t S[n_] := S[n] = Module[{k = 1}, While[True, If[Divisible[k!, n], Return[k], k++]]];
%t a[n_] := S /@ Divisors[2^n] // Total;
%t a /@ Range[0, 52] (* _Jean-François Alcover_, Nov 17 2020 *)
%Y Cf. A029714, A002034.
%K nonn
%O 0,2
%A Norbert Hungerbuhler (buhler(AT)math.ethz.ch)
%E More terms from _R. J. Mathar_, Jun 06 2007
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