A340380 Numbers whose odd part is a squarefree semiprime (A006881); numbers of the form 2^k * p * q, with k >= 0, and distinct odd primes p and q.

15, 21, 30, 33, 35, 39, 42, 51, 55, 57, 60, 65, 66, 69, 70, 77, 78, 84, 85, 87, 91, 93, 95, 102, 110, 111, 114, 115, 119, 120, 123, 129, 130, 132, 133, 138, 140, 141, 143, 145, 154, 155, 156, 159, 161, 168, 170, 174, 177, 182, 183, 185, 186, 187, 190, 201, 203, 204, 205, 209, 213, 215, 217, 219, 220, 221, 222, 228, 230

Offset: 1

Author

Antti Karttunen, Jan 06 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..24567; terms < 2^16

Crossrefs

Cf. A000265, A006881, A280710, A340370 (characteristic function).

Subsequence of A285800, from which this differs for the first time at n=25, where a(25) = 110, while A285800(25) = 105, which is missing from this sequence.

Programs

Mathematica

semiQ[n_] := FactorInteger[n][[;;,2]] == {1, 1}; Select[Range[230], semiQ[#/2^IntegerExponent[#, 2]] &] (* Amiram Eldar, Jan 03 2022 *)

PARI

isA340380(n) = A340370(n); \\ Uses the program given in A340370.

Formula

Sum_{n>=1} 1/a(n)^s = (2^s/(2^s-1)) * ((1/2)*(P(s)^2 - P(2*s)) + 1/4^s - P(s)/2^s), for s>1, where P is the prime zeta function. - Amiram Eldar, Jan 03 2022