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

1,1

Links

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

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

Mathematica

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

Prog

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

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.

Sequence in context: A070537 A324110 A285800 * A184041 A070005 A275384

Adjacent sequences: A340377 A340378 A340379 * A340381 A340382 A340383

Keyword

nonn

Author

Antti Karttunen, Jan 06 2021

Status

approved