

A114636


Numbers n such that nth octagonal number is 8almost prime.


2



22, 70, 80, 84, 102, 108, 118, 126, 134, 160, 174, 184, 200, 230, 240, 250, 252, 262, 264, 272, 318, 330, 334, 336, 350
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..2000
Eric Weisstein's World of Mathematics, Octagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.


FORMULA

n such that n*(3*n2) 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*n2) = 8. n such that [(3*n2)*(3*n1)*(3*n)]/[(3*n2)+(3*n1)+(3*n)] is an element of A046310.


EXAMPLE

a(1) = 22 because OctagonalNumber(22) = Oct(22) = 22*(3*222) = 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*702) = 14560 = 2^5 * 5 * 7 * 13 is 8almost prime.
a(3) = 80 because Oct(80) = 80*(3*802) = 19040 = 2^5 * 5 * 7 * 17.


MATHEMATICA

Select[Range[400], PrimeOmega[PolygonalNumber[8, #]]==8&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 31 2020 *)


CROSSREFS

Cf. A000040, A000567, A001222, A001358, A014612, A014613, A014614, A046306, A046308, A046310.
Sequence in context: A002757 A346854 A041950 * A334034 A044160 A044541
Adjacent sequences: A114633 A114634 A114635 * A114637 A114638 A114639


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Feb 18 2006


STATUS

approved



