A129510 Number of distinct differences between pairs of distinct divisors of n.

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

Offset

1,4

Comments

a(n) = #{|x-y|: 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}:
44-22=22, 44-11=33, 44-4=40, 44-2=42, 44-1=41,
22-11=11, 22-4=18, 22-2=20, 22-1=21,
11-4=7, 11-2=9, 11-1=10, 4-2=2, 4-1=3, 2-1=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}:
45-15=30, 45-9=36, 45-5=40, 45-3=42, 45-1=44,
15-9=6, 15-5=10, 15-3=12, 15-1=14,
9-5=4, 9-3=6, 9-1=8, 5-3=2, 5-1=4, 3-1=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, #d-1, 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