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A114548 Numbers k such that k-th heptagonal number is 3-almost prime.

%I A114548 #22 Feb 16 2025 08:32:59
%S A114548 3,8,11,19,20,25,28,37,38,43,52,58,59,67,68,70,77,82,83,85,86,89,92,
%T A114548 98,106,110,116,124,130,131,133,134,137,139,142,149,157,161,169,172,
%U A114548 179,181,182,185,188,190,193,202,206,209,211,214,217,227,233,238,244
%N A114548 Numbers k such that k-th heptagonal number is 3-almost prime.
%H A114548 Amiram Eldar, <a href="/A114548/b114548.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%H A114548 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%H A114548 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeptagonalNumber.html">Heptagonal Number</a>.
%F A114548 Numbers k such that Hep(k) = k*(5*k-3)/2 is 3-almost prime.
%F A114548 Numbers k such that A000566(k) is a term of A014612.
%F A114548 Numbers k such that A001222(A000566(k)) = 3.
%F A114548 Numbers k such that A001222(k*(5*k-3)/2) = 3.
%e A114548 a(1) = 3 because Hep(3) = 3*(5*3-3)/2 = 18 = 2 * 3^2 is 3-almost prime.
%e A114548 a(2) = 8 because Hep(8) = 8*(5*8-3)/2 = 148 = 2^2 * 37 is 3-almost prime.
%e A114548 a(3) = 11 because Hep(11) = 11*(5*11-3)/2 = 286 = 2 * 11 * 13 is 3-almost prime.
%e A114548 a(17) = 82 because Hep(82) = 82*(5*82-3)/2 = 16687 = 11 * 37 * 41 is 3-almost prime (and 3-brilliant).
%t A114548 Select[Range[400], PrimeOmega[# (5 # - 3)/2] == 3 &] (* _Giovanni Resta_, Jun 14 2016 *)
%t A114548 Select[Range[250],PrimeOmega[PolygonalNumber[7,#]]==3&] (* _Harvey P. Dale_, Sep 04 2020 *)
%Y A114548 Cf. A000040, A000566, A001222, A001358, A014612, A099153.
%K A114548 easy,nonn
%O A114548 1,1
%A A114548 _Jonathan Vos Post_, Feb 15 2006
%E A114548 Corrected and extended by _Giovanni Resta_, Jun 14 2016