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%I A061782 #18 Jul 19 2024 03:14:10
%S A061782 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 A061782 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 A061782 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 A061782 a(n) = smallest positive number m such that m*n is a triangular number.
%H A061782 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 A061782 For p an odd prime, a(p) = (p-1)/2. For nonnegative k, a(2^k) = 2^(k+1)-1.
%F A061782 Formula corrected by Nick Singer, Jun 26 2006
%e A061782 a(4) = 7 as 4*7 = 28 is a triangular number and 7 is the smallest such number.
%p A061782 isA000217 := proc(n)
%p A061782     issqr(1+8*n) ;
%p A061782 end proc:
%p A061782 A061782 := proc(n)
%p A061782     local a;
%p A061782     for a from 1 do
%p A061782         if isA000217(n*a) then
%p A061782             return a;
%p A061782         end if;
%p A061782     end do:
%p A061782 end proc:
%p A061782 seq(A061782(n),n=1..40) ; # _R. J. Mathar_, Oct 03 2014
%t A061782 snt[n_]:=Module[{k=1},While[!OddQ[Sqrt[1+8k n]],k++];k]; Array[snt, 100] (* _Harvey P. Dale_, Feb 15 2017 *)
%Y A061782 Cf. A000217, A011772.
%K A061782 nonn,easy
%O A061782 1,2
%A A061782 _Amarnath Murthy_, May 24 2001
%E A061782 Corrected and extended by _Matthew Conroy_, May 28 2001

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