login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 2

%I #11 Jan 03 2022 07:37:23

%S 15,21,30,33,35,39,42,51,55,57,60,65,66,69,70,77,78,84,85,87,91,93,95,

%T 102,110,111,114,115,119,120,123,129,130,132,133,138,140,141,143,145,

%U 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

%N 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.

%H Antti Karttunen, <a href="/A340380/b340380.txt">Table of n, a(n) for n = 1..24567; terms < 2^16</a>

%F 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

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

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

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

%Y 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.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jan 06 2021

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 25 03:15 EDT 2024. Contains 371964 sequences. (Running on oeis4.)