A094518 Number of pairs (x,y) of divisors of n with x<y such that also x+y is a divisor of n.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 5, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 12, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 11, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 9, 0, 0, 0, 2, 0, 2

Offset

1,12

Comments

a(A094519(n)) > 0, a(A094520(n)) = 0.

a(A097370(n)) = n and a(m) <> n for m < A097370(n).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Example

n=30 with divisor set {1,2,3,5,6,10,15,30}: a(30)=4, as 1<2 & 3=1+2, 1<5 & 6=1+5, 2<3 & 5=2+3 and 5<10 & 15=5+10.

Mathematica

Table[Count[Subsets[#, {2}], _?(Mod[n, Total@ #] == 0 &)] &@ Divisors@ n, {n, 102}] (* Michael De Vlieger, Sep 10 2018 *)

Prog

(PARI) A094518(n) = if(1==n, 0, my(d=divisors(n), c=0); for(i=1, (#d-1), for(j=(i+1), #d, if(!(n%(d[i]+d[j])), c++))); (c)); \\ Antti Karttunen, Sep 10 2018

Crossrefs

Cf. A091009.

Sequence in context: A059484 A360016 A035678 * A123074 A095269 A356302

Adjacent sequences: A094515 A094516 A094517 * A094519 A094520 A094521

Keyword

nonn

Author

Reinhard Zumkeller, May 06 2004

Status

approved