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 A036896 Odd refactorable numbers. 11
 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 1,2 COMMENTS Odd refactorable numbers are always squares. All terms = 1 (mod 8). [Zak Seidov, May 25 2010] LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1001 terms from Harvey P. Dale) S. Colton, Refactorable Numbers - A Machine Invention, J. Integer Sequences, Vol. 2, 1999, #2. 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 October 14 16:48 EDT 2019. Contains 328022 sequences. (Running on oeis4.)