

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



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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}] (* JeanFrançois 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,changed


AUTHOR

Felice Russo, Feb 25 2000


EXTENSIONS

More terms from Matthew M. Conroy, May 13 2001


STATUS

approved



