OFFSET
1,2
COMMENTS
Conjecture: n/a(n) <= 1.6.
Størmer-number-counting function: a(n) is the number of terms in A005528 less than or equal to n. - Luc Rousseau, Jun 13 2018
LINKS
Michel Lagneau, Table of n, a(n) for n = 1..10000
EXAMPLE
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}.
MAPLE
with(numtheory):nn:=100:lst:={}:
for n from 1 to nn do:
p:=n^2+1:x:=factorset(p):n0:=nops(x):
A:={op(x), x[n0]}:
lst:=lst union A :n1:=nops(lst):printf(`%d, `, n1):
od:
MATHEMATICA
Array[Length@ Tally@ First@ Transpose@ Flatten[FactorInteger[#^2 + 1] & /@ Range@ #, 1] &, {69}] (* Michael De Vlieger, Aug 18 2015 *)
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 *)
PROG
(PARI) lista(nn) = {v = []; for (n=1, nn, v = Set(concat(v, factor(n^2+1)[, 1]~)); print1(#v, ", "); ); } \\ Michel Marcus, Aug 16 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 15 2015
STATUS
approved