A264885 Numbers in A007504 such that omega(a(n)) = Omega(a(n)) = 3.

238, 874, 2914, 3266, 3638, 4438, 5117, 6601, 7982, 8582, 9854, 10191, 10538, 10887, 11966, 13101, 17283, 19113, 23069, 38238, 40313, 41741, 46191, 53342, 54998, 56690, 68341, 74139, 80189, 84341, 88585, 90763, 95165, 98534, 100838

Offset: 1

Author

Debapriyay Mukhopadhyay, Nov 27 2015

Keywords

• nonn

Comments

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, ....

Intersection of A007504 and A007304 (sphenic numbers). - Michel Marcus, Dec 15 2015

Examples

			For n = 1, k(n) = 13 and a(n) = A007504(13) = 238 = 2*7*17.
For n = 2, k(n) = 23 and a(n) = A007504(23) = 874 = 2*19*23.
For n = 3, k(n) = 39 and a(n) = A007504(39) = 2914 = 2*31*47.
For n = 4, k(n) = 41 and a(n) = A007504(41) = 3266 = 2*23*71.
For n = 5, k(n) = 43 and a(n) = A007504(43) = 3638 = 2*17*107.
For n = 6, k(n) = 47 and a(n) = A007504(47) = 4438 = 2*7*317.
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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Maple

N:= 10^4: # to use primes up to N
select(t -> numtheory:-bigomega(t)=3 and numtheory:-issqrfree(t),
ListTools:-PartialSums(select(isprime,[2,seq(i,i=3..N,2)]))); # Robert Israel, Dec 15 2015

Mathematica

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 *)

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