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 A261345 #27 Sep 11 2021 17:25:11
%S A261345 1,2,2,3,4,5,5,5,6,7,8,9,9,10,11,12,12,12,13,14,14,15,16,17,18,19,20,
%T A261345 21,22,22,22,22,23,24,25,26,27,27,28,29,29,30,30,31,32,32,32,33,34,34,
%U A261345 35,36,37,38,38,39,39,40,41,42,43,44,45,46,47,48,49,49,50
%N A261345 Number of distinct prime divisors among the numbers k^2 + 1 for k in 1 <= k <= n.
%C A261345 Conjecture: n/a(n) <= 1.6.
%C A261345 Størmer-number-counting function: a(n) is the number of terms in A005528 less than or equal to n. - _Luc Rousseau_, Jun 13 2018
%H A261345 Michel Lagneau, <a href="/A261345/b261345.txt">Table of n, a(n) for n = 1..10000</a>
%e A261345 For a(5), there are 4 distinct prime divisors that occur in the values 1^2+1 = 2, 2^2+1 = 5, 3^2+1 = 2*5, 4^2+1 = 17, 5^2+1 = 26 = 2*13. Taken together, the distinct prime factors are {2,5,13,17}.
%p A261345 with(numtheory):nn:=100:lst:={}:
%p A261345 for n from 1 to nn do:
%p A261345 p:=n^2+1:x:=factorset(p):n0:=nops(x):
%p A261345 A:={op(x),x[n0]}:
%p A261345 lst:=lst union A :n1:=nops(lst):printf(`%d, `,n1):
%p A261345 od:
%t A261345 Array[Length@ Tally@ First@ Transpose@ Flatten[FactorInteger[#^2 + 1] & /@ Range@ #, 1] &, {69}] (* _Michael De Vlieger_, Aug 18 2015 *)
%t A261345 Module[{nn=70,fi},fi=Table[FactorInteger[n^2+1][[All,1]],{n,nn}];Table[ Length[ Union[Flatten[Take[fi,m]]]],{m,nn}]] (* _Harvey P. Dale_, Sep 11 2021 *)
%o A261345 (PARI) lista(nn) = {v = []; for (n=1, nn, v = Set(concat(v, factor(n^2+1)[,1]~)); print1(#v, ", "););} \\ _Michel Marcus_, Aug 16 2015
%Y A261345 Cf. A002144, A002496, A002522, A089122, A005528.
%K A261345 nonn
%O A261345 1,2
%A A261345 _Michel Lagneau_, Aug 15 2015