A091009 Number of triples (u,v,w) of divisors of n with v-u = w-v, and u < v < w.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 1, 0, 2, 0, 0, 3, 0, 0, 7, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 11, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 10, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 9, 0, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0

Offset: 1

Author

Reinhard Zumkeller, Dec 13 2003

Keywords

• nonn

Comments

a(A091014(n))=n and a(m)<>n for m<=A091014(n);

a(A091010(n))=0; a(A091011(n))>0; a(A091012(n))=1; a(A091013(n))>1.

Number of pairs (x,y) of divisors of n with xAntti Karttunen, Sep 10 2018

Examples

			a(30)=4, as there are exactly 4 triples of divisors with the defining property: (1,2,3), (1,3,5), (2,6,10) and (5,10,15).
		

Links

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

Crossrefs

Cf. also A094518.

Programs

Mathematica

Array[Count[Subsets[#, {3}], ?(#2 - #1 == #3 - #2 & @@ # &)] &@ Divisors@ # &, 105] (* _Michael De Vlieger, Sep 10 2018 *)

PARI

A091009(n) = if(1==n,0,my(d=divisors(n),c=0); for(i=1,(#d-1),for(j=(i+1),#d,if(!(n%(d[j]+(d[j]-d[i]))),c++))); (c)); \\ Antti Karttunen, Sep 10 2018

Extensions

Definition clarified by Antti Karttunen, Sep 10 2018