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A264885
Numbers in A007504 such that omega(a(n)) = Omega(a(n)) = 3.
2
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved