A053051 - OEIS

%I #17 Jun 20 2020 15:30:58

%S 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,

%T 24,11,19,46,41,20,43,12,164,13,23,63,41,14,24,76,44,15,80,47,108,67,

%U 16,96,17,109,164,121,42,86,18,89,19,132,46,235,149,150,20,49,281,50

%N 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.

%H T. D. Noe, <a href="/A053051/b053051.txt">Table of n, a(n) for n = 1..1000</a>

%H F. Russo, <a href="http://www.gallup.unm.edu/~smarandache/Felice-Russo-book1.pdf">A set of new Smarandache functions, sequences and conjectures in number theory</a>, American Research Press 2000 .

%e 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.

%t 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 *)

%t 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 *)

%Y Cf. A000005, A002034, A011772, A006218.

%K easy,nice,nonn

%O 1,2

%A _Felice Russo_, Feb 25 2000

%E More terms from Matthew M. Conroy, May 13 2001