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

1,2

Comments

Odd refactorable numbers are always squares.

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A033950, A036896.

Sequence in context: A316751 A001897 A074214 * A129966 A354675 A243128

Adjacent sequences: A036894 A036895 A036896 * A036898 A036899 A036900

Keyword

nonn

Author

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

Status

approved