1,1

It is necessary but not sufficient that n must be prime (A000040), semiprime (A001358), 3-almost prime (A014612), or 4-almost prime (A014613).

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 five prime factors (with multiplicity). n such that A000567(n) is an element of A014614. n such that A001222(A000567(n)) = 5. n such that A001222(n) + A001222(3*n-2) = 5. n such that [(3*n-2)*(3*n-1)*(3*n)]/[(3*n-2)+(3*n-1)+(3*n)] is an element of A014614.

a(1) = 8 because OctagonalNumber(8) = Oct(8) = 8*(3*8-2) = 176 = 2^4 * 11 has exactly 5 prime factors (four are all equally 2; factors need not be distinct). Also, 176 = Oct(8) = Oct(Oct(2)), an iterated octagonal number. Also, 176 is a pengaonal number, hence an element of A046189 octagonal pentagonal numbers.

a(2) = 10 because Oct(10) = 10*(3*10-2) = 280 = 2^3 * 5 * 7 is 5-almost prime.

a(3) = 20 because Oct(20) = 20*(3*20-2) = 1160 = 2^3 * 5 * 29.

a(4) = 26 because Oct(26) = 26*(3*26-2) = 1976 = 2^3 * 13 * 19.

a(17) = 129 because Oct(129) = 129*(3*129-2) = 49665 = 3 * 5 * 7 * 11 * 43 is 5-almost prime (in this case, the 5 prime factors are distinct).

Cf. A000040, A000567, A001222, A001358, A014612, A014613, A014614.

Sequence in context: A090097 A022322 A070974 this_sequence A073619 A032488 A102844

Adjacent sequences: A114618 A114619 A114620 this_sequence A114622 A114623 A114624

easy,nonn

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