A360118 Number of differences (not all necessarily distinct) between consecutive divisors of n which are not also divisors of n.

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

Antti Karttunen, Table of n, a(n) for n = 1..65537

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

Cf. also A060763, A060764, A138652, A360119.

Sequence in context: A340390 A325280 A039803 * A147809 A325144 A328610

Adjacent sequences: A360115 A360116 A360117 * A360119 A360120 A360121

Keyword

nonn

Author

Antti Karttunen, Feb 20 2023

Status

approved