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

1,12

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 x<y such that also 2y-x is a divisor of n. - Antti Karttunen, Sep 10 2018

Links

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

Example

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).

Mathematica

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

Prog

(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

Crossrefs

Cf. also A094518.

Sequence in context: A233286 A305802 A186038 * A204814 A174903 A167163

Adjacent sequences: A091006 A091007 A091008 * A091010 A091011 A091012

Keyword

nonn

Author

Reinhard Zumkeller, Dec 13 2003

Extensions

Definition clarified by Antti Karttunen, Sep 10 2018

Status

approved