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A345211
Numbers with the same number of odd / even, refactorable divisors.
1
2, 4, 6, 10, 14, 18, 20, 22, 26, 28, 30, 34, 38, 42, 44, 46, 50, 52, 54, 58, 62, 66, 68, 70, 74, 76, 78, 82, 86, 90, 92, 94, 98, 100, 102, 106, 110, 114, 116, 118, 122, 124, 126, 130, 134, 138, 140, 142, 146, 148, 150, 154, 158, 162, 164, 166, 170, 172, 174, 178, 182, 186, 188
OFFSET
1,1
COMMENTS
All the terms are even. Conjecture: The sequence a(n)/2 is the complement of A157932 (verified for a(n) < 4*10^7). - Amiram Eldar, Oct 11 2023
LINKS
EXAMPLE
18 is in the sequence since it has 2 odd and 2 even, refactorable divisors: 1, 2, 9, and 18.
MATHEMATICA
q[n_] := DivisorSum[n, (-1)^# &, Divisible[#, DivisorSigma[0, #]] &] == 0; Select[Range[2, 200, 2], q] (* Amiram Eldar, Oct 11 2023 *)
PROG
(PARI) is(n) = (n%2)! && sumdiv(n, d, (-1)^d * !(d % numdiv(d))) == 0; \\ Amiram Eldar, Oct 11 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 10 2021
STATUS
approved