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A360118
Number of differences (not all necessarily distinct) between consecutive divisors of n which are not also divisors of n.
3
0, 0, 1, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 1, 3, 0, 1, 0, 1, 0, 3, 1, 1, 0, 2, 1, 3, 1, 1, 1, 1, 0, 3, 1, 3, 0, 1, 1, 3, 1, 1, 0, 1, 1, 5, 1, 1, 0, 2, 2, 3, 1, 1, 0, 3, 2, 3, 1, 1, 0, 1, 1, 5, 0, 3, 1, 1, 1, 3, 4, 1, 0, 1, 1, 5, 1, 3, 1, 1, 2, 4, 1, 1, 1, 3, 1, 3, 1, 1, 1, 3, 1, 3, 1, 3, 0, 1, 2, 5, 0, 1, 1, 1, 1, 7
OFFSET
1,9
LINKS
FORMULA
For all n >= 1, A060763(n) <= a(n) < A060764(n).
a(n) = A060764(n) - A360119(n).
EXAMPLE
For n=70, its divisors are {1, 2, 5, 7, 10, 14, 35, 70} and their first differences are {1, 3, 2, 3, 4, 21, 35}, of which the differences {3, 3, 4, 21} are not divisors, so a(70) = 4. Note that in contrast to A060763, here the difference 3 is counted twice because there are two copies of it among the differences.
PROG
(PARI) A360118(n) = { my(d=divisors(n), erot = vector(#d-1, k, d[k+1] - d[k])); sum(i=1, #erot, !!(n%erot[i])); };
CROSSREFS
Sequence in context: A340390 A325280 A039803 * A147809 A325144 A328610
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 20 2023
STATUS
approved