A036897 Square root of odd refactorable numbers.

1, 3, 15, 21, 25, 33, 39, 45, 51, 57, 69, 75, 81, 87, 93, 111, 123, 129, 141, 159, 177, 183, 189, 201, 213, 219, 225, 237, 249, 267, 291, 303, 309, 315, 321, 327, 339, 343, 381, 393, 405, 411, 417, 447, 453, 471, 489, 495, 501, 519, 525, 537, 543, 567, 573

Offset: 1

Author

Simon Colton (simonco(AT)cs.york.ac.uk)

Keywords

• nonn

Comments

Odd refactorable numbers are always squares.

Examples

			15^2 is refactorable because 225 has 9 divisors and 9 divides 225.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1001
• S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.
• S. Colton, HR - Automatic Theory Formation in Pure Mathematics

Crossrefs

Cf. A033950, A036896.

Programs

Mathematica

Select[Range[1, 1000, 2], Divisible[#^2, DivisorSigma[0,#^2]] &] (* Amiram Eldar, Jul 02 2019 *)

PARI

isrefac(n) = ! (n % numdiv(n));
lista(nn) = {forstep (n = 1, nn, 2, if (isrefac(n), print1(sqrtint(n), ", ")););} \\ Michel Marcus, Aug 31 2013

Formula

a(n) = sqrt(A036896(n)). - Amiram Eldar, Jul 02 2019