A073331 - OEIS

A073331

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).

1, 1, 2, 11, 3, 57, 2, 3, 6, 1013, 2, 4083, 50, 1, 2, 65519, 2, 262125, 61, 43, 1002, 4194281, 2, 23, 4070, 9, 36, 268435427, 51, 1073741793, 8, 991, 65502, 29, 8, 68719476699, 262106, 4057, 41, 1099511627735, 22, 4398046511061, 980, 5, 4194258, 70368744177617

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OFFSET

2,3

LINKS

Amiram Eldar, Table of n, a(n) for n = 2..100

MATHEMATICA

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 *)

CROSSREFS

Cf. A000005, A002034, A073307, A073413, A073535.

Sequence in context: A241596 A365769 A339616 * A109858 A082266 A070840

Adjacent sequences: A073328 A073329 A073330 * A073332 A073333 A073334

KEYWORD

nonn

AUTHOR

Jason Earls, Aug 22 2002

EXTENSIONS

More terms from Sean A. Irvine, Feb 20 2011

a(37)-a(47) from Amiram Eldar, Jan 20 2019

STATUS

approved