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A036896 Odd refactorable numbers. 10
1, 9, 225, 441, 625, 1089, 1521, 2025, 2601, 3249, 4761, 5625, 6561, 7569, 8649, 12321, 15129, 16641, 19881, 25281, 31329, 33489, 35721, 40401, 45369, 47961, 50625, 56169, 62001, 71289, 84681, 91809, 95481, 99225, 103041, 106929, 114921 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Odd refactorable numbers are always squares.

All terms = 1 (mod 8). [Zak Seidov, May 25 2010]

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2.

S. Colton, HR - Automatic Theory Formation in Pure Mathematics

EXAMPLE

9 is refactorable because tau(9)=3 and 3 divides 9.

MATHEMATICA

Do[If[IntegerQ[n/DivisorSigma[0, n]], Print[n]], {n, 1, 100000, 2}]

Select[Range[1, 1001, 2]^2, Divisible[#, DivisorSigma[0, #]]&] (* Harvey P. Dale, Jan 22 2012 *)

PROG

(PARI) is(n)=n%2&&issquare(n)&&n%numdiv(n)==0 \\ Charles R Greathouse IV, Apr 23 2013

(PARI) list(lim)=my(v=List(), f); forstep(n=1, sqrtint(lim\1), 2, f=factor(n)[, 2]; if(n^2%prod(i=1, #f, 2*f[i]+1)==0, listput(v, n^2))); Vec(v) \\ Charles R Greathouse IV, Apr 23 2013

CROSSREFS

Subsequence of A033950 and of A016754.

Sequence in context: A264848 A033632 A110260 * A120319 A057530 A014736

Adjacent sequences:  A036893 A036894 A036895 * A036897 A036898 A036899

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)