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%I #14 Jun 03 2021 14:33:00
%S 1,3,1,7,2,1,3,15,4,1,5,3,6,2,1,31,8,2,9,6,1,3,11,5,12,3,13,1,14,4,15,
%T 63,2,4,3,1,18,5,2,3,20,5,21,12,1,6,23,11,24,6,3,15,26,7,1,21,3,7,29,
%U 2,30,8,6,127,5,1,33,2,4,3,35,28,36,9,4,21,3,1,39,26,40,10,41,14,7,11,5
%N a(n) = smallest positive number m such that m*n is a triangular number.
%H Alois P. Heinz, <a href="/A061782/b061782.txt">Table of n, a(n) for n = 1..20000</a> (first 1000 terms from Harvey P. Dale)
%F For p an odd prime, a(p) = (p-1)/2. For nonnegative k, a(2^k) = 2^(k+1)-1.
%F Formula corrected by Nick Singer, Jun 26 2006
%e a(4) = 7 as 4*7 = 28 is a triangular number and 7 is the smallest such number.
%p isA000217 := proc(n)
%p issqr(1+8*n) ;
%p end proc:
%p A016782 := proc(n)
%p local a;
%p for a from 1 do
%p if isA000217(n*a) then
%p return a;
%p end if;
%p end do:
%p end proc:
%p seq(A016782(n),n=1..40) ; # _R. J. Mathar_, Oct 03 2014
%t snt[n_]:=Module[{k=1},While[!OddQ[Sqrt[1+8k n]],k++];k]; Array[snt, 100] (* _Harvey P. Dale_, Feb 15 2017 *)
%Y Cf. A000217, A011772.
%K nonn,easy
%O 1,2
%A _Amarnath Murthy_, May 24 2001
%E Corrected and extended by _Matthew Conroy_, May 28 2001
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