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A250069
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a(n) = n^2 mod gpf(n^2 + 1) where gpf(k) is the greatest prime dividing k.
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1
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1, 4, 4, 16, 12, 36, 4, 12, 40, 100, 60, 28, 16, 196, 112, 256, 28, 12, 180, 400, 16, 96, 52, 576, 312, 676, 72, 156, 420, 52, 36, 40, 108, 88, 612, 1296, 136, 16, 760, 1600, 28, 352, 36, 148, 1012, 72, 16, 460, 1200, 60, 1300, 540, 280, 2916, 88, 3136, 12
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OFFSET
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1,2
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COMMENTS
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For n > 1, a(n) == 0 (mod 4).
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LINKS
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FORMULA
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a(n) = n^2 mod A014442(n) where A014442(n) is the greatest prime factor of n^2 + 1.
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EXAMPLE
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a(5)=12 because 5^2 mod A014442(5) = 25 mod 13 = 12.
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MAPLE
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with(numtheory):
for n from 1 to 500 do:
p:=n^2+1:x:=factorset(p):n0:=nops(x):r:=irem(n^2, x[n0]):
printf(`%d, `, r):
od:
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MATHEMATICA
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Table[Mod[n^2, FactorInteger[n^2+1, FactorComplete->True][[-1, 1]]], {n, 100}]
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PROG
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(PARI) a(n) = lift(Mod(n, vecmax(factor(n^2+1)[, 1]))^2); \\ Michel Marcus, Sep 13 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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Edited: exchanged name with an old comment. Old name as an alternative formula. Keyword easy added. - Wolfdieter Lang, Nov 29 2014
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STATUS
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approved
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