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
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Simon Colton (simonco(AT)cs.york.ac.uk)
STATUS
approved