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A180772 Number of distinct solutions to the congruence x(1)*x(2) == 0 (mod n), with x() only in 1..n-1. 1
0, 0, 0, 1, 0, 2, 0, 3, 3, 4, 0, 9, 0, 6, 8, 10, 0, 15, 0, 17, 12, 10, 0, 27, 10, 12, 15, 25, 0, 38, 0, 26, 20, 16, 24, 51, 0, 18, 24, 51, 0, 56, 0, 41, 51, 22, 0, 74, 21, 50, 32, 49, 0, 69, 40, 75, 36, 28, 0, 121, 0, 30, 75, 68, 48, 92, 0, 65, 44, 106, 0, 141, 0, 36, 90, 73, 60, 110, 0, 138 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Also, number of ordered pairs (a, b) with 0 < a <= b such that a*b = c*n + d and c = d where 0 < a, b, c, d < n. - Naohiro Nomoto, Oct 02 2021

LINKS

R. H. Hardin, Table of n, a(n) for n=1..10000

FORMULA

a(n) = A174088(n) - n = ( A018804(n) + A000188(n) )/2 - n.

EXAMPLE

The a(12)=9 solutions for product of a single 1..11 pair == 0 (mod 12) are 2*6, 3*4, 3*8, 4*6, 4*9, 6*6, 6*8, 6*10, and 8*9.

CROSSREFS

Column 1 of A180782.

Cf. A000188, A018804, A174088.

Sequence in context: A239313 A046667 A108407 * A291304 A245332 A202035

Adjacent sequences:  A180769 A180770 A180771 * A180773 A180774 A180775

KEYWORD

nonn

AUTHOR

R. H. Hardin, formula from Max Alekseyev in the Sequence Fans Mailing List, Sep 20 2010

STATUS

approved

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Last modified July 4 10:11 EDT 2022. Contains 355075 sequences. (Running on oeis4.)