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 A105551 #22 Feb 16 2025 08:32:57
%S A105551 1,1,1,1,1,2,2,1,1,1,1,1,2,1,1,1,1,1,2,2,2,2,2,2,2,2,2,1,1,1,2,2,1,1,
%T A105551 1,1,1,2,2,2,2,2,2,2,3,2,1,1,1,1,3,2,2,2,2,1,3,3,2,1,2,1,1,3,2,3,1,2,
%U A105551 1,1,3,2,1,2,3,2,2,2,1,3,1,1,3,2,1,2
%N A105551 Number of distinct prime factors of n^3 + n^2 + 71.
%C A105551 This cubic equation with small positive coefficients is strangely rich in primes and semiprimes. The first 44 consecutive values, for n = 0, 1, 2, ..., 43, are all either prime (23 of them) or semiprime (21 of them), before the first 3-almost prime value is encountered.
%H A105551 T. D. Noe, <a href="/A105551/b105551.txt">Table of n, a(n) for n = 0..1000</a>
%H A105551 Ulrich Abel and Hartmut Siebert, <a href="https://www.jstor.org/stable/2323773">Sequences with Large Numbers of Prime Values</a>, Am. Math. Monthly 100, 167-169, 1993.
%H A105551 Robin Forman, <a href="https://www.jstor.org/stable/2324063">Sequences with Many Primes</a>, Amer. Math. Monthly 99, 548-557, 1992.
%H A105551 Betty Garrison, <a href="https://www.jstor.org/stable/2324515">Polynomials with Large Numbers of Prime Values</a>, Amer. Math. Monthly 97, 316-317, 1990.
%H A105551 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>.
%F A105551 a(n) = A001221(n^3 + n^2 + 71).
%e A105551 a(0) = 1 because 0^3 + 0^2 + 71 = 71 is prime.
%e A105551 a(1) = 1 because 1^3 + 1^2 + 71 = 73 is prime.
%e A105551 a(2) = 1 because 2^3 + 2^2 + 71 = 83 is prime.
%e A105551 a(3) = 1 because 3^3 + 3^2 + 71 = 107 is prime.
%e A105551 a(4) = 1 because 3^3 + 3^2 + 71 = 151 is prime.
%e A105551 a(5) = 2 because 3^3 + 3^2 + 71 = 221 = 13 * 17 is the first semiprime.
%e A105551 a(44) = 3 because 44^3 + 44^2 + 71 = 87191 = 13 * 19 * 353 is the first 3-almost prime for nonnegative integers n.
%t A105551 Table[PrimeNu[n^3+n^2+71],{n,0,90}] (* _Harvey P. Dale_, Oct 09 2012 *)
%o A105551 (PARI) a(n)=omega(n^3 + n^2 + 71) \\ _Charles R Greathouse IV_, Jan 31 2017
%Y A105551 Cf. A000040, A001358, A005846, A007635, A007641, A048988, A050265, A050268, A050267, A050266.
%K A105551 easy,nonn
%O A105551 0,6
%A A105551 _Jonathan Vos Post_, May 03 2005
%E A105551 More terms from _Robert G. Wilson v_, May 21 2005