cp's OEIS Frontend

A114635 Numbers k such that the k-th octagonal number is 7-almost prime.

%I A114635 #17 Feb 16 2025 08:32:59
%S A114635 24,30,32,38,48,66,72,78,90,94,104,110,112,114,120,136,140,154,164,
%T A114635 166,168,176,180,190,204,206,208,210,220,222,228,238,248,254,276,280,
%U A114635 284,286,290,300,306,312,326,338,344
%N A114635 Numbers k such that the k-th octagonal number is 7-almost prime.
%C A114635 It is necessary but not sufficient that k must be prime (A000040), semiprime (A001358), 3-almost prime (A014612), 4-almost prime (A014613), 5-almost prime (A014614), or 6-almost prime (A046308).
%H A114635 Amiram Eldar, <a href="/A114635/b114635.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%H A114635 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%H A114635 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>.
%F A114635 Numbers k such that k*(3*k-2) has exactly seven prime factors (with multiplicity).
%F A114635 Numbers k such that A000567(k) is a term of A046308.
%F A114635 Numbers k such that A001222(A000567(k)) = 7.
%F A114635 Numbers k such that A001222(k) + A001222(3*k-2) = 7.
%F A114635 Numbers k such that [(3*k-2)*(3*k-1)*(3*k)]/[(3*k-2)+(3*k-1)+(3*k)] is a term of A046308.
%e A114635 a(1) = 24 because OctagonalNumber(24) = Oct(24) = 24*(3*24-2) = 96 = 1680 = 2^4 * 3 * 5 * 7 has exactly 7 prime factors (four are all equally 2; factors need not be distinct).
%e A114635 a(2) = 30 because Oct(30) = 30*(3*30-2) = 2640 = 2^4 * 3 * 5 * 11 is 7-almost prime.
%e A114635 a(3) = 32 because Oct(32) = 32*(3*32-2) = 3008 = 2^6 * 47 is 7-almost prime.
%t A114635 Select[Range[400],PrimeOmega[PolygonalNumber[8,#]]==7&] (* _Harvey P. Dale_, Aug 13 2021 *)
%Y A114635 Cf. A000040, A000567, A001222, A001358, A014612, A014613, A014614, A046306, A046308.
%K A114635 easy,nonn
%O A114635 1,1
%A A114635 _Jonathan Vos Post_, Feb 18 2006