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A114556 Numbers n such that n-th heptagonal number is 5-almost prime. 1
7, 16, 23, 30, 32, 36, 42, 45, 54, 69, 78, 79, 80, 84, 88, 90, 93, 95, 100, 102, 104, 112, 115, 117, 140, 143, 151, 153, 165, 170, 174, 176, 184, 186, 191, 200, 203, 210, 213, 228, 232, 234, 245, 250, 259, 271, 273, 282, 287, 296, 306, 308, 310, 311, 318, 319 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Hep(2) = 7 is the only prime heptagonal number.
LINKS
Eric Weisstein's World of Mathematics, Heptagonal Number.
Eric Weisstein's World of Mathematics, Almost Prime.
FORMULA
n such that Hep(n) = n*(5*n-3)/2 is 5-almost prime. n such that A000566(n) is an element of A014614. n such that A001222(A000566(n)) = 5. n such that A001222(n*(5*n-3)/2) = 5.
EXAMPLE
a(1) = 7 because Hep(7) = 7*(5*7-3)/2 = 112 = 2^4 * 7 is 5-almost prime [also 112 = Hep(7) = Hep(Hep(2)) is an iterated heptagonal number].
a(2) = 16 because Hep(16) = 16*(5*16-3)/2 = 616 = 2^3 * 7 * 11 is 5-almost prime.
a(3) = 23 because Hep(23) = 23*(5*23-3)/2 = 1288 = 2^3 * 7 * 23.
a(18) = 100 because Hep(100) = 100*(5*100-3)/2 = 24850 = 2 * 5^2 * 7 * 71.
a(21) = 112 because Hep(112) = 112*(5*112-3)/2 = 31192 = 2^3 * 7 * 557 [also 31192 = Hep(112) = Hep(Hep(7)) = Hep(Hep(Hep(2))) is an iterated heptagonal number].
MATHEMATICA
Select[Range[400], PrimeOmega[# (5 # - 3)/2] == 5 &] (* Giovanni Resta, Jun 14 2016 *)
Select[Range[400], PrimeOmega[PolygonalNumber[7, #]]==5&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 22 2020 *)
CROSSREFS
Sequence in context: A342743 A368407 A044440 * A136772 A190371 A367084
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 15 2006
EXTENSIONS
Corrected and extended by Giovanni Resta, Jun 14 2016
STATUS
approved

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Last modified February 23 04:31 EST 2024. Contains 370267 sequences. (Running on oeis4.)