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A240884
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Semiprimes of the form C(n) + T(n) where C(n) and T(n) are the n-th cube and triangular numbers.
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5
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33, 74, 237, 371, 1055, 1397, 10901, 12443, 30287, 39899, 55613, 80453, 207149, 303041, 360467, 407999, 639797, 1230821, 1650053, 2056511, 2695349, 2873441, 3454427, 3956873, 9823349, 10384103, 13680599, 15844877, 16419449, 20608499, 22705373, 26508143
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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);
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MATHEMATICA
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KD = {}; Do[t = n^3 + n/2*(n + 1); If[PrimeOmega[t] == 2, AppendTo[KD, t]], {n, 500}]; KD
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PROG
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(PARI) has(n)=if(n%2, isprime(n) && isprime(n^2+n\2+1), isprime(n/2) && isprime(2*n^2+n+1))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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