

A091009


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


9



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
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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 2yx 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, (#d1), 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



