A184481 Semiprime centered triangular numbers.

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.

Links

Table of n, a(n) for n=1..55.

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

Cf. A001358, A005448, A125602.

Sequence in context: A155223 A155219 A153985 * A149227 A149228 A149229

Adjacent sequences: A184478 A184479 A184480 * A184482 A184483 A184484

Keyword

nonn,easy

Author

Jonathan Vos Post, Feb 12 2011

Status

approved