1,1

It is necessary but not sufficient that n must be prime (A000040), semiprime (A001358), or 3-almost prime (A014612).

Eric Weisstein's World of Mathematics, Octagonal Number.

Eric Weisstein's World of Mathematics, Almost Prime.

n such that n*(3*n-2) has exactly four prime factors (with multiplicity). n such that A000567(n) is an element of A014613. n such that A001222(A000567(n)) = 4. n such that A001222(n) + A001222(3*n-2) = 4. n such that [(3*n-2)*(3*n-1)*(3*n)]/[(3*n-2)+(3*n-1)+(3*n)] is an element of A014613.

a(1) = 4 because OctagonalNumber(4) = Oct(4) = 4*(3*4-2) = 40 = 2^3 * 5 has exactly 4 prime factors (3 are all equally 2; factors need not be distinct).

a(2) = 9 because Oct(9) = 9*(3*9-2) = 225 = 3^2 * 5^2, a 4-almost prime [225 is also a square, hence a square octagonal number A036428, as is Oct(121)].

a(3) = 27 because Oct(27) = 27*(3*27-2) = 2133 = 3^3 * 79.

a(4) = 39 because Oct(39) = 39*(3*39-2) = 4485 = 3 * 5 * 13 * 23 has exactly 4 prime factors, in this case distinct.

a(26) = 187 because Oct(187) = 187*(3*187-2) = 104533 = 11 * 13 * 17 * 43 [a 4-brilliant number, that is with 4 prime factors that are each the same number of digits in length].

Cf. A000040, A000567, A001222, A001358, A014612, A014613, A036428.

Sequence in context: A113682 A145855 A099615 this_sequence A067758 A034527 A111962

Adjacent sequences: A114615 A114616 A114617 this_sequence A114619 A114620 A114621

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 17 2006