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A174088
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Number of pairs (i,j) such that i*j == 0 (mod k), 0 <= i <= j < k.
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2
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1, 2, 3, 5, 5, 8, 7, 11, 12, 14, 11, 21, 13, 20, 23, 26, 17, 33, 19, 37, 33, 32, 23, 51, 35, 38, 42, 53, 29, 68, 31, 58, 53, 50, 59, 87, 37, 56, 63, 91, 41, 98, 43, 85, 96, 68, 47, 122, 70, 100, 83, 101, 53, 123, 95, 131, 93, 86, 59, 181, 61, 92, 138, 132, 113, 158, 67, 133, 113
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OFFSET
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1,2
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COMMENTS
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a(p) = p for p prime, since gcd(k,p) = 1 for 1 <= k < p, the product of k is also coprime to p, but multiples n*p for n >= 1 are plainly divisible by p. - Michael De Vlieger, Nov 22 2019
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LINKS
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FORMULA
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MATHEMATICA
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Table[If[PrimeQ@ b, b, Count[Flatten@ Array[# Range@ # &, b], _?(Mod[#, b] == 0 &)]], {b, 69}] (* Michael De Vlieger, Nov 22 2019 *)
f1[p_, e_] := (e*(p - 1)/p + 1)*p^e; f2[p_, e_] := p^Floor[e/2]; a[n_] := (Times @@ f1 @@@ (fct = FactorInteger[n]) + Times @@ f2 @@@ fct)/2; Array[a, 100] (* Amiram Eldar, Apr 28 2023 *)
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PROG
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(PARI) a(n)={ my(ct=0); for(i=0, n-1, for(j=0, i, ct+=(Mod(i*j, n)==0) ) ); ct; } \\ Joerg Arndt, Aug 03 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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