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A367804
Numbers that are both exponentially odd (A268335) and exponentially evil (A262675).
4
1, 8, 27, 32, 125, 216, 243, 343, 512, 864, 1000, 1331, 1944, 2197, 2744, 3125, 3375, 4000, 4913, 6859, 7776, 9261, 10648, 10976, 12167, 13824, 16807, 17576, 19683, 24389, 25000, 27000, 29791, 30375, 32768, 35937, 39304, 42592, 42875, 50653, 54872, 59319, 64000
OFFSET
1,2
COMMENTS
Numbers whose prime factorization contains only exponents that are odd evil numbers (A129771).
LINKS
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
Intersection of A262675 and A268335.
Cf. A129771.
Sequence in context: A370788 A304291 A056824 * A361268 A355038 A297868
KEYWORD
nonn,easy,base
AUTHOR
Amiram Eldar, Dec 01 2023
STATUS
approved