OFFSET
1,1
COMMENTS
The n-th triangular number T(n) = n/2*(n+1).
All the terms in the sequence, except a(2), are odd.
Semiprimes (biprimes) in the sequence are product of two primes and simultaneously sum of n-th cube & triangular numbers.
LINKS
K. D. Bajpai, Table of n, a(n) for n = 1..6556
EXAMPLE
a(1) = 33: 3^3 + 3/2*(3+1) = 33 = 3*11, which is product of two primes and hence semiprime.
a(3) = 237: 6^3 + 6/2*(6+1) = 237 = 3*79, which is product of two primes and hence semiprime.
MAPLE
with(numtheory):KD:= proc() local a, b; a:=(n)^3+n/2*(n+1); b:=bigomega(a); if b=2 then RETURN (a); fi; end: seq(KD(), n=1..500);
MATHEMATICA
KD = {}; Do[t = n^3 + n/2*(n + 1); If[PrimeOmega[t] == 2, AppendTo[KD, t]], {n, 500}]; KD
PROG
(PARI) has(n)=if(n%2, isprime(n) && isprime(n^2+n\2+1), isprime(n/2) && isprime(2*n^2+n+1))
for(n=1, 1e4, if(has(n), print1(n^3+n*(n+1)/2", "))) \\ Charles R Greathouse IV, Aug 25 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
K. D. Bajpai, Apr 14 2014
STATUS
approved