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%I #19 Jan 20 2019 10:14:06
%S 1,1,2,11,3,57,2,3,6,1013,2,4083,50,1,2,65519,2,262125,61,43,1002,
%T 4194281,2,23,4070,9,36,268435427,51,1073741793,8,991,65502,29,8,
%U 68719476699,262106,4057,41,1099511627735,22,4398046511061,980,5,4194258,70368744177617
%N Smallest k such that S(n) = d(n+k), where S(n) is the Kempner function (A002034) and d(n) is the number of divisors of n (A000005).
%H Amiram Eldar, <a href="/A073331/b073331.txt">Table of n, a(n) for n = 2..100</a>
%t kemp[n_] := Module[{m = 1}, While[!IntegerQ[m!/n], m++]; m]; a[n_] := Module[{k = 1, s = kemp[n]}, While[DivisorSigma[0, n + k] != s, k++]; k]; Array[a, 20, 2] (* _Amiram Eldar_, Jan 20 2019 *)
%Y Cf. A000005, A002034, A073307, A073413, A073535.
%K nonn
%O 2,3
%A _Jason Earls_, Aug 22 2002
%E More terms from _Sean A. Irvine_, Feb 20 2011
%E a(37)-a(47) from _Amiram Eldar_, Jan 20 2019
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