login
A114548
Numbers k such that k-th heptagonal number is 3-almost prime.
1
3, 8, 11, 19, 20, 25, 28, 37, 38, 43, 52, 58, 59, 67, 68, 70, 77, 82, 83, 85, 86, 89, 92, 98, 106, 110, 116, 124, 130, 131, 133, 134, 137, 139, 142, 149, 157, 161, 169, 172, 179, 181, 182, 185, 188, 190, 193, 202, 206, 209, 211, 214, 217, 227, 233, 238, 244
OFFSET
1,1
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, Heptagonal Number.
FORMULA
Numbers k such that Hep(k) = k*(5*k-3)/2 is 3-almost prime.
Numbers k such that A000566(k) is a term of A014612.
Numbers k such that A001222(A000566(k)) = 3.
Numbers k such that A001222(k*(5*k-3)/2) = 3.
EXAMPLE
a(1) = 3 because Hep(3) = 3*(5*3-3)/2 = 18 = 2 * 3^2 is 3-almost prime.
a(2) = 8 because Hep(8) = 8*(5*8-3)/2 = 148 = 2^2 * 37 is 3-almost prime.
a(3) = 11 because Hep(11) = 11*(5*11-3)/2 = 286 = 2 * 11 * 13 is 3-almost prime.
a(17) = 82 because Hep(82) = 82*(5*82-3)/2 = 16687 = 11 * 37 * 41 is 3-almost prime (and 3-brilliant).
MATHEMATICA
Select[Range[400], PrimeOmega[# (5 # - 3)/2] == 3 &] (* Giovanni Resta, Jun 14 2016 *)
Select[Range[250], PrimeOmega[PolygonalNumber[7, #]]==3&] (* Harvey P. Dale, Sep 04 2020 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 15 2006
EXTENSIONS
Corrected and extended by Giovanni Resta, Jun 14 2016
STATUS
approved