

A129510


Number of distinct differences between pairs of distinct divisors of n.


6



0, 1, 1, 3, 1, 5, 1, 6, 3, 6, 1, 10, 1, 6, 5, 10, 1, 13, 1, 13, 6, 6, 1, 18, 3, 6, 6, 14, 1, 19, 1, 15, 6, 6, 6, 24, 1, 6, 6, 22, 1, 23, 1, 15, 12, 6, 1, 30, 3, 15, 6, 15, 1, 25, 6, 23, 6, 6, 1, 37, 1, 6, 13, 21, 6, 25, 1, 15, 6, 24, 1, 40, 1, 6, 13, 15, 6, 26, 1, 34, 10, 6, 1, 45, 6, 6, 6, 26
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OFFSET

1,4


COMMENTS

a(n) = #{xy: x <> y and n mod x = n mod y = 0};
a(n) = 1 iff n is prime;
a(n) <= A000217(A000005(a(n))1) = A066446(n):
a(A129511(n))=A066446(A129511(n)), a(A129512(n)) < A066446(A129512(n)).


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Divisor


EXAMPLE

n=44, set of divisors of 44 = {1,2,4,11,22,44}:
4422=22, 4411=33, 444=40, 442=42, 441=41,
2211=11, 224=18, 222=20, 221=21,
114=7, 112=9, 111=10, 42=2, 41=3, 21=1,
a(44) = #{1,2,3,7,9,10,11,18,20,21,22,33,40,41,42} = 15;
n=45, set of divisors of 45 = {1,3,5,9,15,45}:
4515=30, 459=36, 455=40, 453=42, 451=44,
159=6, 155=10, 153=12, 151=14,
95=4, 93=6, 91=8, 53=2, 51=4, 31=2,
a(45) = #{2,4,6,8,10,12,14,30,36,40,42,44} = 12.


PROG

(PARI) a(n)=my(d=divisors(n), v=List()); for(i=1, #d1, for(j=i+1, #d, listput(v, d[j]d[i]))); #Set(v) \\ Charles R Greathouse IV, Aug 26 2015


CROSSREFS

Cf. A000005.
Sequence in context: A029652 A238952 A333976 * A225656 A087913 A090585
Adjacent sequences: A129507 A129508 A129509 * A129511 A129512 A129513


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Apr 19 2007


STATUS

approved



