OFFSET
1,1
COMMENTS
The n-th triangular number T(n) = n/2*(n+1).
Semiprimes (biprimes) in the sequence are product of two primes, simultaneously sum of n-th square & triangular numbers.
All the terms in the sequence, except a(2), are odd numbers.
LINKS
K. D. Bajpai, Table of n, a(n) for n = 1..9010
EXAMPLE
a(1) = 15: 3^2 + 3/2*(3+1) = 15 = 3*5, which is product of two primes. Hence it is semiprime.
a(3) = 57: 6^2 + 6/2*(6+1) = 57 = 3*19, which is product of two primes. Hence it is semiprime.
MAPLE
with(numtheory):KD:= proc() local a, b; a:=(n)^2 + 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^2 + n/2*(n + 1); If[PrimeOmega[t] == 2, AppendTo[KD, t]], {n, 500}]; KD
c=0; Do[t=n^2 + n/2*(n+1); If[PrimeOmega[t]==2, c=c+1; Print[c, " ", t]], {n, 1, 500000}];
Module[{nn=500, s, t}, s=Range[nn]^2; t=Accumulate[Range[nn]]; Select[ Total/@ Thread[{s, t}], PrimeOmega[#]==2&]] (* or *) Select[ Table[ (n(1+3n))/2, {n, 500}], PrimeOmega[#]==2&](* Harvey P. Dale, Feb 07 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
K. D. Bajpai, Apr 14 2014
STATUS
approved