A066561 a(n) is the smallest triangular number divisible by n.

1, 6, 3, 28, 10, 6, 21, 120, 36, 10, 55, 36, 78, 28, 15, 496, 136, 36, 171, 120, 21, 66, 253, 120, 300, 78, 351, 28, 406, 120, 465, 2016, 66, 136, 105, 36, 666, 190, 78, 120, 820, 210, 903, 528, 45, 276, 1081, 528, 1176, 300, 153, 780, 1378, 378, 55, 1176, 171

Offset: 1

Author

Amarnath Murthy, Dec 17 2001

Keywords

• nonn

Comments

See A344005 for an efficient algorithm. - N. J. A. Sloane, Jul 13 2021

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000217, A011772, A344005, A345988.

Programs

PARI

{ for (n=1, 1000, s=0; b=0; while (b==0, s++; t=s*(s+1)/2; if (t%n == 0, b=1)); write("b066561.txt", n, " ", t) ) } \\ Harry J. Smith, Mar 05 2010

Formula

a(n) = A000217(A011772(n)). - Bill McEachen, Dec 28 2021

a(n) = A344005(2*n)*(A344005(2*n)+1)/2. - Chai Wah Wu, Apr 21 2025

Extensions

More terms from Naohiro Nomoto, Dec 26 2001