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A114618 Numbers n such that n-th octagonal number is 4-almost prime. 1
4, 9, 27, 39, 49, 57, 59, 69, 75, 85, 87, 105, 109, 117, 119, 121, 125, 143, 147, 153, 161, 169, 175, 177, 185, 187, 199, 207, 217, 219, 231, 235, 239, 245, 249, 265, 267, 269, 275, 283, 285, 289, 291, 299, 301, 305, 311, 319, 321, 327, 329, 333, 335, 345, 349, 357, 359, 361, 363, 371, 381, 385 (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), or 3-almost prime (A014612).

LINKS

Table of n, a(n) for n=1..62.

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 four prime factors (with multiplicity). n such that A000567(n) is an element of A014613. n such that A001222(A000567(n)) = 4. n such that A001222(n) + A001222(3*n-2) = 4. n such that [(3*n-2)*(3*n-1)*(3*n)]/[(3*n-2)+(3*n-1)+(3*n)] is an element of A014613.

EXAMPLE

a(1) = 4 because OctagonalNumber(4) = Oct(4) = 4*(3*4-2) = 40 = 2^3 * 5 has exactly 4 prime factors (3 are all equally 2; factors need not be distinct).

a(2) = 9 because Oct(9) = 9*(3*9-2) = 225 = 3^2 * 5^2, a 4-almost prime [225 is also a square, hence a square octagonal number A036428, as is Oct(121)].

a(3) = 27 because Oct(27) = 27*(3*27-2) = 2133 = 3^3 * 79.

a(4) = 39 because Oct(39) = 39*(3*39-2) = 4485 = 3 * 5 * 13 * 23 has exactly 4 prime factors, in this case distinct.

a(26) = 187 because Oct(187) = 187*(3*187-2) = 104533 = 11 * 13 * 17 * 43 [a 4-brilliant number, that is with 4 prime factors that are each the same number of digits in length].

MATHEMATICA

Select[Range[400], PrimeOmega[#(3#-2)]==4&] (* Harvey P. Dale, Sep 07 2011 *)

CROSSREFS

Cf. A000040, A000567, A001222, A001358, A014612, A014613, A036428.

Sequence in context: A145855 A240042 A099615 * A067758 A304677 A214418

Adjacent sequences:  A114615 A114616 A114617 * A114619 A114620 A114621

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Feb 17 2006

EXTENSIONS

265 inserted by R. J. Mathar, Dec 22 2010

STATUS

approved

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Last modified August 15 13:11 EDT 2020. Contains 336504 sequences. (Running on oeis4.)