A053051 Smallest integer m such that sum_(k=1 to m) d(k) is divisible by n, where d(k) (A000005) is the number of divisors of k.

1, 4, 2, 4, 3, 19, 6, 4, 10, 5, 20, 19, 17, 6, 15, 7, 32, 48, 23, 8, 24, 20, 9, 42, 16, 17, 10, 24, 11, 19, 46, 41, 20, 43, 12, 164, 13, 23, 63, 41, 14, 24, 76, 44, 15, 80, 47, 108, 67, 16, 96, 17, 109, 164, 121, 42, 86, 18, 89, 19, 132, 46, 235, 149, 150, 20, 49, 281, 50

Offset

1,2

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

F. Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press 2000 .

Example

a(1)=1 since 1 has 1 divisor; a(3)=2 since 1 has 1 divisor, 2 has 2 divisors and 1+2=3; a(2)=4 since 1+2+2+3=8, a multiple of 4, while 1, 1+2 and 1+2+2 are not multiples of 4.

Mathematica

a[n_] := (m = 1; While[ !Divisible[ Sum[ DivisorSigma[0, k], {k, 1, m}], n], m++]; m); Table[ a[n], {n, 1, 69}] (* Jean-François Alcover, Dec 28 2011 *)
Module[{nn=300, d}, d=Accumulate[DivisorSigma[0, Range[nn]]]; Table[ SelectFirst[ Thread[{d, Range[nn]}], Divisible[#[[1]], n]&], {n, 70}]][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 20 2020 *)

Crossrefs

Cf. A000005, A002034, A011772, A006218.

Sequence in context: A083954 A038702 A085062 * A075234 A232715 A317951

Adjacent sequences: A053048 A053049 A053050 * A053052 A053053 A053054

Keyword

easy,nice,nonn

Author

Felice Russo, Feb 25 2000

Extensions

More terms from Matthew M. Conroy, May 13 2001

Status

approved