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A114636 Numbers n such that n-th octagonal number is 8-almost 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), 3-almost prime (A014612), 4-almost prime (A014613), 5-almost prime (A014614), 6-almost prime (A046306), or 7-almost 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*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.

EXAMPLE

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.

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

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Last modified May 27 16:48 EDT 2022. Contains 354110 sequences. (Running on oeis4.)