A061782 a(n) = smallest positive number m such that m*n is a triangular number.

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, 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, 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

Offset: 1

Author

Amarnath Murthy, May 24 2001

Keywords

• nonn
• easy

Examples

			a(4) = 7 as 4*7 = 28 is a triangular number and 7 is the smallest such number.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000 (first 1000 terms from Harvey P. Dale)

Crossrefs

Cf. A000217, A011772.

Programs

Maple

isA000217 := proc(n)
    issqr(1+8*n) ;
end proc:
A061782 := proc(n)
    local a;
    for a from 1 do
        if isA000217(n*a) then
            return a;
        end if;
    end do:
end proc:
seq(A061782(n),n=1..40) ; # R. J. Mathar, Oct 03 2014

Mathematica

snt[n_]:=Module[{k=1},While[!OddQ[Sqrt[1+8k n]],k++];k]; Array[snt, 100] (* Harvey P. Dale, Feb 15 2017 *)

Formula

For p an odd prime, a(p) = (p-1)/2. For nonnegative k, a(2^k) = 2^(k+1)-1.

Formula corrected by Nick Singer, Jun 26 2006

Extensions

Corrected and extended by Matthew Conroy, May 28 2001