OFFSET
1,2
COMMENTS
Numbers whose prime factorization contains only exponents that are odd evil numbers (A129771).
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
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + Sum_{k>=1} 1/p^A129771(k)) = Product_{p prime} f(1/p) = 1.22183814098622400889..., where f(x) = 1 + (2*x/(1-x^2) + Product_{k>=0} (1 - x^(2^k)) - Product_{k>=0} (1 - (-x)^(2^k)))/4.
MATHEMATICA
q[n_] := OddQ[n] && EvenQ[DigitCount[n, 2, 1]]; Select[Range[150], #== 1 || AllTrue[FactorInteger[#][[;; , 2]], q] &]
PROG
(PARI) is(n) = {my(f = factor(n)); for (i = 1, #f~, if(!(f[i, 2]%2) || hammingweight(f[i, 2])%2, return (0))); 1; }
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Amiram Eldar, Dec 01 2023
STATUS
approved