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), or 7-almost prime (A046308).

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 eight prime factors (with multiplicity). n such that A000567(n) is an element of A046310. n such that A001222(A000567(n)) = 8. n such that A001222(n) + A001222(3*n-2) = 8. 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) = 22 because OctagonalNumber(22) = Oct(22) = 22*(3*22-2) = 1408 = 2^7 * 11 has exactly 8 prime factors (seven are all equally 2; factors need not be distinct).

a(2) = 70 because Oct(70) = 70*(3*70-2) = 14560 = 2^5 * 5 * 7 * 13 is 8-almost prime.

a(3) = 80 because Oct(80) = 80*(3*80-2) = 19040 = 2^5 * 5 * 7 * 17.

Cf. A000040, A000567, A001222, A001358, A014612, A014613, A014614, A046306, A046308, A046310.

Sequence in context: A041948 A002757 A041950 this_sequence A044160 A044541 A080861

Adjacent sequences: A114633 A114634 A114635 this_sequence A114637 A114638 A114639

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 18 2006