

A174088


Number of pairs (i,j) such that i*j == 0 (mod k), 0 <= i <= j < k.


2



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

1,2


COMMENTS

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


LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = ( A018804(n) + A000188(n) ) / 2.  Max Alekseyev, Sep 05 2010


MATHEMATICA

Table[If[PrimeQ@ b, b, Count[Flatten@ Array[# Range@ # &, b], _?(Mod[#, b] == 0 &)]], {b, 69}] (* Michael De Vlieger, Nov 22 2019 *)


PROG

(PARI) a(n)={ my(ct=0); for(i=0, n1, for(j=0, i, ct+=(Mod(i*j, n)==0) ) ); ct; } \\ Joerg Arndt, Aug 03 2013


CROSSREFS

Sequence in context: A063914 A209187 A166250 * A304493 A208323 A067284
Adjacent sequences: A174085 A174086 A174087 * A174089 A174090 A174091


KEYWORD

nonn


AUTHOR

Russell Easterly, Mar 06 2010


EXTENSIONS

More terms from Max Alekseyev, Sep 05 2010
Better name from Joerg Arndt, Aug 03 2013


STATUS

approved



