OFFSET
1,2
COMMENTS
Numbers whose prime factorization contains only exponents that are even evil numbers (A125592).
Also, squares of exponentially evil numbers (A262675).
Also, numbers with an equal number of exponentially odious and exponentially evil divisors, i.e., numbers k such that A366901(k) = A366902(k). - Amiram Eldar, Feb 26 2024
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Vladimir Shevelev, S-exponential numbers, Acta Arithmetica, Vol. 175 (2016), pp. 385-395.
FORMULA
MATHEMATICA
evilQ[n_] := EvenQ[DigitCount[n, 2, 1]]; Select[Range[10^4]^2, #== 1 || AllTrue[FactorInteger[#][[;; , 2]], evilQ] &]
PROG
(PARI) isexpevil(n) = {my(f = factor(n)); for (i = 1, #f~, if(hammingweight(f[i, 2])%2, return (0))); 1; }
is(n) = issquare(n) && isexpevil(n);
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Amiram Eldar, Dec 01 2023
STATUS
approved