A367804 Numbers that are both exponentially odd (A268335) and exponentially evil (A262675).

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

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

Intersection of A262675 and A268335.

Cf. A367801, A367802, A367803.

Cf. A129771.

Sequence in context: A370788 A304291 A056824 * A361268 A355038 A297868

Adjacent sequences: A367801 A367802 A367803 * A367805 A367806 A367807

Keyword

nonn,easy,base

Author

Amiram Eldar, Dec 01 2023

Status

approved