1,1

It is necessary but not sufficient that n must be prime (A000040), semiprime (A001358), 3-almost prime (A014612), 4-almost prime (A014613), 5-almost prime (A014614), 6-almost prime (A046306), 7-almost prime (A046308), or 8-almost prime (A046310).

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 nine prime factors (with multiplicity). n such that A000567(n) is an element of A046312. n such that A001222(A000567(n)) = 9. n such that A001222(n) + A001222(3*n-2) = 9. n such that [(3*n-2)*(3*n-1)*(3*n)]/[(3*n-2)+(3*n-1)+(3*n)] is an element of A046310.

a(1) = 64 because OctagonalNumber(64) = Oct(64) = 64*(3*64-2) = 12160 = 2^7 * 5 * 19 has exactly 9 prime factors (seven are all equally 2; factors need not be distinct).

a(2) = 96 because Oct(96) = 96*(3*96-2) = 27456 = 2^6 * 3 * 11 * 13 is 9-almost prime [also 27456 = Oct(96) = Oct(Oct(6)) is an iterated octagonal number].

a(3) = 128 because Oct(128) = 128*(3*128-2) = 48896 = 2^8 * 191.

Cf. A000040, A000567, A001222, A001358, A014612, A014613, A014614, A046306, A046308, A046310, A046312, A088878, A114606, A114618, A114621, A114634, A114635, A114636.

Sequence in context: A114407 A114417 A046305 this_sequence A036330 A046306 A104022

Adjacent sequences: A114825 A114826 A114827 this_sequence A114829 A114830 A114831

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 19 2006