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, ....
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
KEYWORD
nonn
AUTHOR
Debapriyay Mukhopadhyay, Nov 27 2015
STATUS
approved