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 A242012 a(n) is the number of positive integers k <= n for which gpf(k^2 + 1) = gpf(n^2 + 1), where gpf is the greatest prime divisor. 3
 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 4, 1, 1, 3, 1, 3, 1, 1, 2, 5, 1, 1, 2, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 4, 1, 3, 3, 1, 2, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) = 1 if n is a term in A005574 (numbers n such that n^2 + 1 is prime). a(n) = 1 if gpf(k^2 + 1) <> gpf(n^2 + 1) for every positive integer k < n. LINKS Michel Lagneau, Table of n, a(n) for n = 1..10000 EXAMPLE a(3) = 2 because the greatest prime divisor of 3^2 + 1 is 5 and n=3 is the 2nd positive value of n at which gpf(n^2 + 1) = 5; the 1st is n=2: gpf(2^2 + 1) = 5. a(313) = 7 because the greatest prime divisor of 313^2 + 1 is 101, and n=313 is the 7th positive value of n at which this occurs:    10^2 + 1 = 101;    91^2 + 1 = 2 * 41 * 101;   111^2 + 1 = 2 * 61 * 101;   192^2 + 1 = 5 * 73 * 101;   212^2 + 1 = 5 * 89 * 101;   293^2 + 1 = 2 * 5^2 * 17 * 101;   313^2 + 1 = 2 * 5 * 97 * 101. MAPLE with(numtheory):nn:=200:T:=array(1..nn):k:=0: for m from 1 to nn do: x:=factorset(m^2+1):n1:=nops(x):p:=x[n1]:k:=k+1:T[k]:=p: od:   for n from 1 to 150 do:   q:=T[n]:ii:=0:     for i from 1 to n do:       if T[i]=q then ii:=ii+1:       else       fi:     od:     printf(`%d, `, ii):   od: # Simpler version: N:= 1000:  # to get a(n) for n <= N T:= Array(1..N): for n from 1 to N do T[n]:= max(numtheory:-factorset(n^2+1));   A[n]:= numboccur(T, T[n]); od: seq(A[n], n=1..N); # Robert Israel, Aug 12 2014 PROG (PARI) a(n) = my(gn = vecmax(factor(n^2+1)[, 1])); sum(k=1, n, vecmax(factor(k^2+1)[, 1]) == gn); \\ Michel Marcus, Sep 10 2017 CROSSREFS Cf. A002496, A005574, A014442. Sequence in context: A072776 A077481 A278113 * A086290 A136568 A152157 Adjacent sequences:  A242009 A242010 A242011 * A242013 A242014 A242015 KEYWORD nonn AUTHOR Michel Lagneau, Aug 11 2014 EXTENSIONS Edited by Jon E. Schoenfield, Sep 10 2017 STATUS approved

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Last modified August 7 19:28 EDT 2020. Contains 336279 sequences. (Running on oeis4.)