|
%I #33 Mar 29 2017 05:01:32
%S 5830,6870,13490,16401,58406,60146,61910,65534,75130,136114,148827,
%T 153178,213538,257358,269074,273054,327198,354102,377310,382038,
%U 403611,443685,475323,488774,496905,665130,684510,691026,799846,817563
%N Numbers in A007504 such that omega(a(n)) = Omega(a(n)) = 4.
%C Omega and omega are given in A001221 and A001222, respectively.
%C 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 Intersection of A007504 and A046386 (products of four distinct primes). - _Michel Marcus_, Dec 15 2015
%H John Cerkan, <a href="/A264887/b264887.txt">Table of n, a(n) for n = 1..10000</a>
%e For n = 1, k(n) = 53 and a(n) = A007504(53) = 5830 = 2*5*11*53.
%e For n = 2, k(n) = 57 and a(n) = A007504(57) = 6870 = 2*3*5*229.
%e For n = 3, k(n) = 77 and a(n) = A007504(77) = 13490 = 2*5*19*71.
%e For n = 4, k(n) = 84 and a(n) = A007504(84) = 16401 = 3*7*11*71.
%e For n = 5, k(n) = 149 and a(n) = A007504(149) = 58406 = 2*19*29*53.
%e For n = 6, k(n) = 151 and a(n) = A007504(151) = 60146 = 2*17*29*61.
%e 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 t = Accumulate@ Prime@ Range@ 600; Select[t, PrimeNu@ # == PrimeOmega@ # == 4 &] (* _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) == 4) && (bigomega(s)==4), print1(s, ", ")););} \\ _Michel Marcus_, Nov 28 2015
%Y Cf. A001221, A001222, A007504, A013918, A046386, A189072, A264885.
%K nonn
%O 1,1
%A _Debapriyay Mukhopadhyay_, Nov 27 2015
|
