A261476 -id:A261476 - cp's OEIS frontend

A261488 Number of triples (x, y, x mod y) such that x > y are divisors of n and x mod y is an anti-divisor of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 3, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 3, 0, 1, 0, 0, 0, 0

Offset: 1

Juri-Stepan Gerasimov, Aug 20 2015

nonn

An anti-divisor of n is a number d in the range [2,n-1] which does not divide n and is either a (necessarily odd) divisor of 2n-1 or 2n+1, or a (necessarily even) divisor of 2n.

a(n) = 0 if n is a prime power.

			a(45) = 2 with triples (5, 3, 5 mod 3) and (15, 9, 15 mod 9) since 3, 5, 9, and 15 are divisors of 45 and 5 mod 3 = 2 and 15 mod 9 = 6 are anti-divisors of 45.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A027750, A130799, A260073, A261476.

a(n)=my(d=divisors(n)); sum(i=1,#d-1, sum(j=i+1,#d, my(z=d[j]%d[i]); z && n%z && if(z%2, (2*n+1)%z==0 || (2*n-1)%z==0, (2*n)%z==0))) \\ Charles R Greathouse IV, Aug 26 2015

A261868 Least number with exactly n triples {x, y, x mod y} of three distinct divisors.

Original entry on oeis.org

1, 6, 28, 12, 56, 40, 24, 66, 30, 36, 48, 224, 160, 1196, 392, 96, 200, 198, 72, 276, 90, 126, 84, 60, 156, 400, 1330, 728, 280, 144, 324, 440, 910, 1000, 520, 552, 216, 378, 462, 264, 456, 168, 288, 120, 546, 798, 330, 210

Offset: 0

Juri-Stepan Gerasimov, Sep 03 2015

Cf. A260073, A261476.

cp's OEIS Frontend

A261488 Number of triples (x, y, x mod y) such that x > y are divisors of n and x mod y is an anti-divisor of n.

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A261868 Least number with exactly n triples {x, y, x mod y} of three distinct divisors.

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