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

5830, 6870, 13490, 16401, 58406, 60146, 61910, 65534, 75130, 136114, 148827, 153178, 213538, 257358, 269074, 273054, 327198, 354102, 377310, 382038, 403611, 443685, 475323, 488774, 496905, 665130, 684510, 691026, 799846, 817563

Offset: 1

Author

Debapriyay Mukhopadhyay, Nov 27 2015

Keywords

• nonn

Comments

Omega and omega are given in A001221 and A001222, respectively.

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, ...

Intersection of A007504 and A046386 (products of four distinct primes). - Michel Marcus, Dec 15 2015

Examples

			For n = 1, k(n) = 53 and a(n) = A007504(53) = 5830 = 2*5*11*53.
For n = 2, k(n) = 57 and a(n) = A007504(57) = 6870 = 2*3*5*229.
For n = 3, k(n) = 77 and a(n) = A007504(77) = 13490 = 2*5*19*71.
For n = 4, k(n) = 84 and a(n) = A007504(84) = 16401 = 3*7*11*71.
For n = 5, k(n) = 149 and a(n) = A007504(149) = 58406 = 2*19*29*53.
For n = 6, k(n) = 151 and a(n) = A007504(151) = 60146 = 2*17*29*61.
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.
		

Links

• John Cerkan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A001222, A007504, A013918, A046386, A189072, A264885.

Programs

Mathematica

t = Accumulate@ Prime@ Range@ 600; Select[t, PrimeNu@ # == PrimeOmega@ # == 4 &] (* Michael De Vlieger, Nov 27 2015, after Zak Seidov at A007504 *)

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