A264885 - OEIS

%I #33 Mar 01 2016 23:59:57

%S 238,874,2914,3266,3638,4438,5117,6601,7982,8582,9854,10191,10538,

%T 10887,11966,13101,17283,19113,23069,38238,40313,41741,46191,53342,

%U 54998,56690,68341,74139,80189,84341,88585,90763,95165,98534,100838

%N Numbers in A007504 such that omega(a(n)) = Omega(a(n)) = 3.

%C The corresponding numbers of prime summands, k(n), are 13, 23, 39, 41, 43, 47, 50, 56, 61, 63, 67, 68, 69, 70, 73, 76, 86, 90, 98, 123, 126, 128, 134, 143, 145, 147, 160, 166, 172, 176, 180, 182, 186, 189, 191, 196, 197, 200, 215, 220, 222, 225, 229, 238, 241, 251, 252, 265, 266, 267, ....

%C Intersection of A007504 and A007304 (sphenic numbers). - _Michel Marcus_, Dec 15 2015

%H Robert Israel, <a href="/A264885/b264885.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 1, k(n) = 13 and a(n) = A007504(13) = 238 = 2*7*17.

%e For n = 2, k(n) = 23 and a(n) = A007504(23) = 874 = 2*19*23.

%e For n = 3, k(n) = 39 and a(n) = A007504(39) = 2914 = 2*31*47.

%e For n = 4, k(n) = 41 and a(n) = A007504(41) = 3266 = 2*23*71.

%e For n = 5, k(n) = 43 and a(n) = A007504(43) = 3638 = 2*17*107.

%e For n = 6, k(n) = 47 and a(n) = A007504(47) = 4438 = 2*7*317.

%e Note that for each of the elements of the sequence, omega(a(n)) = Omega(a(n)) = 3, i.e., the number of prime factors of a(n) = the number of distinct prime factors of a(n) = 3.

%p N:= 10^4: # to use primes up to N

%p select(t -> numtheory:-bigomega(t)=3 and numtheory:-issqrfree(t),

%p ListTools:-PartialSums(select(isprime,[2,seq(i,i=3..N,2)]))); # _Robert Israel_, Dec 15 2015

%t t = Accumulate@ Prime@ Range@ 300; Select[Range[2*10^5], And[MemberQ[t, #], PrimeNu@ # == PrimeOmega@ # == 3] &] (* _Michael De Vlieger_, Nov 27 2015, after _Zak Seidov_ at A007504 *)

%o (PARI) lista(nn) = {my(s = 0); for (n=1, nn, s += prime(n); if ((omega(s) == 3) && (bigomega(s)==3), print1(s, ", ")););} \\ _Michel Marcus_, Nov 28 2015

%Y Cf. A001221, A001222, A007304, A007504, A013918, A189072, A264887.

%K nonn

%O 1,1

%A _Debapriyay Mukhopadhyay_, Nov 27 2015