OFFSET
1,1
COMMENTS
Semiprimes among pentagonal numbers A000326 = { (3*n^2-n)/2; n >= 0 }.
We can have an odd prime n = 2k + 1 and (3n - 1)/2 = 3k + 1 also prime, i.e., k in A130800, or n = 2p with p prime and 3n - 1 = 6p - 1 also prime, i.e., p in A158015. Considering the ratio of the two prime factors, the two possibilities are mutually exclusive, so this is the disjoint union of {A033570(n)=(2n+1)(3n+1); n in A130800} = A255584 and {p*(6p-1); p in A158015}. - M. F. Hasler, Dec 13 2019
LINKS
K. D. Bajpai, Table of n, a(n) for n = 1..10400
EXAMPLE
n=6: (3*n^2-n)/2 = 51 = 3 * 17 which is semiprime. Hence, 51 appears in the sequence.
n=10: (3*n^2-n)/2 = 145 = 5 * 29 which is semiprime. Hence, 145 appears in the sequence.
MATHEMATICA
Select[Table[(3*n^2 - n)/2, {n, 500}], PrimeOmega[#] == 2 &]
PROG
(PARI) select(n->bigomega(n)==2, vector(1000, n, (3*n^2-n)/2)) \\ Colin Barker, Jul 20 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Jul 19 2014
STATUS
approved