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

1,1

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A229077 A129124 A124169 * A252910 A252905 A122266

Adjacent sequences: A264882 A264883 A264884 * A264886 A264887 A264888

Keyword

nonn

Author

Debapriyay Mukhopadhyay, Nov 27 2015

Status

approved