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A264887 Numbers in A007504 such that omega(a(n)) = Omega(a(n)) = 4.

%I A264887 #33 Mar 29 2017 05:01:32
%S A264887 5830,6870,13490,16401,58406,60146,61910,65534,75130,136114,148827,
%T A264887 153178,213538,257358,269074,273054,327198,354102,377310,382038,
%U A264887 403611,443685,475323,488774,496905,665130,684510,691026,799846,817563
%N A264887 Numbers in A007504 such that omega(a(n)) = Omega(a(n)) = 4.
%C A264887 Omega and omega are given in A001221 and A001222, respectively.
%C A264887 The corresponding numbers of prime summands, k(n), are 53, 57, 77, 84, 149, 151, 153, 157, 167, 219, 228, 231, 269, 293, 299, 301, 327, 339, 349, 351, 360, 376, 388, 393, 396, 453, 459, 461, 493, 498, ...
%C A264887 Intersection of A007504 and A046386 (products of four distinct primes). - _Michel Marcus_, Dec 15 2015
%H A264887 John Cerkan, <a href="/A264887/b264887.txt">Table of n, a(n) for n = 1..10000</a>
%e A264887 For n = 1, k(n) = 53 and a(n) = A007504(53) = 5830 = 2*5*11*53.
%e A264887 For n = 2, k(n) = 57 and a(n) = A007504(57) = 6870 = 2*3*5*229.
%e A264887 For n = 3, k(n) = 77 and a(n) = A007504(77) = 13490 = 2*5*19*71.
%e A264887 For n = 4, k(n) = 84 and a(n) = A007504(84) = 16401 = 3*7*11*71.
%e A264887 For n = 5, k(n) = 149 and a(n) = A007504(149) = 58406 = 2*19*29*53.
%e A264887 For n = 6, k(n) = 151 and a(n) = A007504(151) = 60146 = 2*17*29*61.
%e A264887 Note that for each of the elements of the sequence, omega(a(n)) = Omega(a(n)) = 4, i.e., the number of prime factors of a(n) = the number of distinct prime factors of a(n) = 4.
%t A264887 t = Accumulate@ Prime@ Range@ 600; Select[t, PrimeNu@ # == PrimeOmega@ # == 4 &] (* _Michael De Vlieger_, Nov 27 2015, after _Zak Seidov_ at A007504 *)
%o A264887 (PARI) lista(nn) = {my(s = 0); for (n=1, nn, s += prime(n); if ((omega(s) == 4) && (bigomega(s)==4), print1(s, ", ")););} \\ _Michel Marcus_, Nov 28 2015
%Y A264887 Cf. A001221, A001222, A007504, A013918, A046386, A189072, A264885.
%K A264887 nonn
%O A264887 1,1
%A A264887 _Debapriyay Mukhopadhyay_, Nov 27 2015