This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A114618 #19 Feb 16 2025 08:32:59 %S A114618 4,9,27,39,49,57,59,69,75,85,87,105,109,117,119,121,125,143,147,153, %T A114618 161,169,175,177,185,187,199,207,217,219,231,235,239,245,249,265,267, %U A114618 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 %N A114618 Numbers k such that the k-th octagonal number is 4-almost prime. %C A114618 It is necessary but not sufficient that k must be prime (A000040), semiprime (A001358), or 3-almost prime (A014612). %H A114618 Amiram Eldar, <a href="/A114618/b114618.txt">Table of n, a(n) for n = 1..10000</a> %H A114618 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>. %H A114618 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number</a>. %F A114618 Numbers k such that k*(3*k-2) has exactly four prime factors (with multiplicity). %F A114618 Numbers k such that A000567(k) is a term of A014613. %F A114618 Numbers k such that A001222(A000567(k)) = 4. %F A114618 Numbers k such that A001222(k) + A001222(3*k-2) = 4. %F A114618 Numbers k such that [(3*k-2)*(3*k-1)*(3*k)]/[(3*k-2)+(3*k-1)+(3*k)] is a term of A014613. %e A114618 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). %e A114618 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)]. %e A114618 a(3) = 27 because Oct(27) = 27*(3*27-2) = 2133 = 3^3 * 79. %e A114618 a(4) = 39 because Oct(39) = 39*(3*39-2) = 4485 = 3 * 5 * 13 * 23 has exactly 4 prime factors, in this case distinct. %e A114618 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]. %t A114618 Select[Range[400],PrimeOmega[#(3#-2)]==4&] (* _Harvey P. Dale_, Sep 07 2011 *) %Y A114618 Cf. A000040, A000567, A001222, A001358, A014612, A014613, A036428. %K A114618 easy,nonn %O A114618 1,1 %A A114618 _Jonathan Vos Post_, Feb 17 2006 %E A114618 265 inserted by _R. J. Mathar_, Dec 22 2010