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A215935
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Number of ordered pairs of primes (p, q) dividing n for which p^e = 1 mod q, where e is the exponent of p in n.
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2
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0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 1, 2, 1, 1, 0, 3, 0, 1, 1, 0, 0, 2, 0, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 3, 0, 2, 0, 1, 0, 4, 0, 1, 0, 1, 0, 2, 0, 1, 1
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OFFSET
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1,12
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COMMENTS
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If n in A056867 then a(n) = 0.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..10000
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EXAMPLE
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12 is divisible by two primes, 2 and 3. The exponent of 2 is 2 and the exponent of 3 is 1. 2^2 = 1 mod 3 and 3^1 = 1 mod 2, so a(12) = 2.
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MAPLE
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a:= proc(n) local l; l:= ifactors(n)[2];
add(add(`if`(irem(i[1]^i[2], j[1])=1, 1, 0), i=l), j=l)
end:
seq (a(n), n=1..100); # Alois P. Heinz, Aug 28 2012
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MATHEMATICA
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a[n_] := With[{f = FactorInteger[n]}, Sum[ Boole[ Mod[p[[1]]^p[[2]], q[[1]]] == 1], {p, f}, {q, f}]]; Table[a[n], {n, 1, 93}] (* Jean-François Alcover, Sep 03 2012 *)
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PROG
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(PARI) a(n)=my(f=factor(n), k=#f~); sum(i=1, k, sum(j=1, k, i!=j && Mod(f[i, 1], f[j, 1])^f[i, 2]==1))
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CROSSREFS
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Cf. A054395, A056867.
Sequence in context: A161520 A070097 A202523 * A270573 A096271 A285640
Adjacent sequences: A215932 A215933 A215934 * A215936 A215937 A215938
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KEYWORD
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nonn
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AUTHOR
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Charles R Greathouse IV, Aug 27 2012
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STATUS
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approved
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