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A184481
Semiprime centered triangular numbers.
1
4, 10, 46, 85, 166, 235, 274, 361, 514, 694, 901, 1135, 1219, 1306, 1585, 1891, 2461, 2839, 3106, 3385, 3826, 3979, 4135, 5311, 5674, 6049, 6241, 6835, 7246, 8551, 9481, 10966, 11485, 11749, 12286, 12559, 13969, 15151, 15454, 17335, 18649, 18985, 19666, 21421, 21781, 22879, 23626, 24385, 26734, 27949, 28774, 30034, 32194, 33079, 33526
OFFSET
1,1
COMMENTS
Numbers of the form 3*n*(n-1)/2 + 1 = p*q where p and q are primes, not necessarily distinct. This is to semiprimes A001358 as A125602 is to primes A000040.
FORMULA
A001358 INTERSECTION A005448.
EXAMPLE
a(3) = 3*6(6-1)/2 + 1 = 10 = 2 * 5.
MATHEMATICA
SemiprimeQ[n_] := Total[FactorInteger[n]][[2]] == 2; Select[Table[3*n (n - 1)/2 + 1, {n, 150}], SemiprimeQ]
Select[Table[(3n(n-1))/2+1, {n, 200}], PrimeOmega[#]==2&] (* Harvey P. Dale, May 13 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Feb 12 2011
STATUS
approved