A175706 Semiprimes of the form m*p such that k*p=(m*p)-th semiprime.

4, 6, 10, 14, 15, 22, 38, 57, 58, 62, 69, 82, 85, 123, 129, 142, 158, 178, 194, 202, 203, 205, 214, 218, 221, 254, 274, 295, 303, 327, 339, 346, 365, 411, 413, 422, 437, 478, 482, 485, 519, 543, 545, 551, 622, 626, 635, 694, 723, 734, 745, 753, 794, 813, 893

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

a(1)=4 because 5*2=(2*2)-th semiprime, a(2)=6 because 5*3=(2*3)-th semiprime, a(3)=10 because 13*2=(5*2)-th semiprime, a(4)=14 because 19*2=(7*2)-th semiprime, a(5)=15 because 13*3=(5*3)-th semiprime, a(6)=22 because 31*2=(11*2)-th semiprime.

Maple

Contribution from R. J. Mathar, Aug 10 2010: (Start)
A001358 := proc(n) option remember; local a; if n = 1 then 4; else for a from procname(n-1)+1 do if numtheory[bigomega](a) = 2 then return a; end if; end do: end if; end proc:
for i from 1 to 300 do mp := A001358(i) ; kp := A001358(mp) ; p := igcd(mp, kp) ; if isprime(p) then printf("%d, ", mp) ; end if; end do: (End)

Mathematica

SemiPrimeQ[n_Integer] := If[Abs[n]<2, False, (2==Plus@@Transpose[FactorInteger[Abs[n]]][[2]])]; sp=Select[Range[10000], SemiPrimeQ]; sp2=Select[sp, #<Length[sp]&]; Select[sp2, GCD[ #, sp[[ # ]]]>1&] (* T. D. Noe, Aug 11 2010 *)

Prog

(PARI) first(n) = {my(t = 0, res = List()); for(i = 1, oo, if(bigomega(i) == 2, t++; if(bigomega(t) == 2 && gcd(t, i) > 1, listput(res, t); if(#res >= n, return(res) ) ) ); ); res } \\ David A. Corneth, Mar 15 2023

Crossrefs

Cf. A000040, A001358.

Sequence in context: A359157 A084997 A300912 * A110507 A224467 A134624

Adjacent sequences: A175703 A175704 A175705 * A175707 A175708 A175709

Keyword

nonn,less

Author

Juri-Stepan Gerasimov, Aug 10 2010

Extensions

Corrected and extended by R. J. Mathar and T. D. Noe, Aug 11 2010

Status

approved