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 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 (list; graph; refs; listen; history; text; internal format)
 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: A324896 A029652 A238952 * A225656 A087913 A090585 Adjacent sequences:  A129507 A129508 A129509 * A129511 A129512 A129513 KEYWORD nonn AUTHOR Reinhard Zumkeller, Apr 19 2007 STATUS approved

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Last modified June 25 23:52 EDT 2019. Contains 324367 sequences. (Running on oeis4.)