OFFSET
1,1
COMMENTS
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
Eric Weisstein's World of Mathematics, Almost Prime.
Eric Weisstein's World of Mathematics, Octagonal Number.
FORMULA
Numbers k such that k*(3*k-2) has exactly seven prime factors (with multiplicity).
Numbers k such that [(3*k-2)*(3*k-1)*(3*k)]/[(3*k-2)+(3*k-1)+(3*k)] is a term of A046308.
EXAMPLE
a(1) = 24 because OctagonalNumber(24) = Oct(24) = 24*(3*24-2) = 96 = 1680 = 2^4 * 3 * 5 * 7 has exactly 7 prime factors (four are all equally 2; factors need not be distinct).
a(2) = 30 because Oct(30) = 30*(3*30-2) = 2640 = 2^4 * 3 * 5 * 11 is 7-almost prime.
a(3) = 32 because Oct(32) = 32*(3*32-2) = 3008 = 2^6 * 47 is 7-almost prime.
MATHEMATICA
Select[Range[400], PrimeOmega[PolygonalNumber[8, #]]==7&] (* Harvey P. Dale, Aug 13 2021 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 18 2006
STATUS
approved