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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

%I #16 Feb 21 2023 11:43:38

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A360118/b360118.txt">Table of n, a(n) for n = 1..65537</a>

%F For all n >= 1, A060763(n) <= a(n) < A060764(n).

%F a(n) = A060764(n) - A360119(n).

%e 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.

%o (PARI) A360118(n) = { my(d=divisors(n), erot = vector(#d-1, k, d[k+1] - d[k])); sum(i=1,#erot,!!(n%erot[i])); };

%Y Cf. also A060763, A060764, A138652, A360119.

%K nonn

%O 1,9

%A _Antti Karttunen_, Feb 20 2023

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Last modified June 11 19:50 EDT 2024. Contains 373317 sequences. (Running on oeis4.)