A036896 Odd refactorable numbers.
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
Offset: 1
Examples
9 is refactorable because tau(9)=3 and 3 divides 9.
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.
- S. Colton, HR - Automatic Theory Formation in Pure Mathematics
Programs
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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 *) -
PARI
is(n)=n%2&&issquare(n)&&n%numdiv(n)==0 \\ Charles R Greathouse IV, Apr 23 2013
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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
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Python
from itertools import count, islice from math import prod from sympy import factorint def A036896_gen(): # generator of terms for n in count(1,2): if not (m:=n**2)%prod(e<<1|1 for e in factorint(n).values()): yield m A036896_list = list(islice(A036896_gen(),40)) # Chai Wah Wu, Oct 04 2024
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