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A036896
Odd refactorable numbers.
14
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
1,2
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
A036896_list = list(islice(A036896_gen(), 40)) # Chai Wah Wu, Oct 04 2024
CROSSREFS
Subsequence of A033950 and of A016754.
Sequence in context: A264848 A033632 A110260 * A120319 A057530 A014736
KEYWORD
nonn,easy
AUTHOR
Simon Colton (simonco(AT)cs.york.ac.uk)
STATUS
approved