A332810 Number of integers in range 1..n that are not encountered on any of the possible paths from n to 1 when iterating with nondeterministic map k -> k - k/p, where p is any prime factor of k.

0, 0, 0, 1, 1, 1, 1, 4, 3, 4, 4, 5, 5, 5, 5, 11, 11, 9, 9, 12, 9, 12, 12, 15, 16, 15, 17, 16, 16, 16, 16, 26, 16, 26, 17, 24, 24, 24, 24, 30, 30, 25, 25, 31, 27, 31, 31, 37, 31, 38, 37, 38, 38, 40, 39, 41, 40, 41, 41, 42, 42, 42, 43, 57, 43, 43, 43, 58, 43, 46, 46, 57, 57, 57, 54, 58, 47, 58, 58, 68, 66, 68, 68, 62, 69, 62, 62, 72, 72

Offset

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = n - A332809(n).

Example

a(12): we have three alternative paths: {12, 8, 4, 2, 1}, {12, 6, 4, 2, 1} or {12, 6, 3, 2, 1}, with [5, 7, 9, 10, 11] being the only numbers in range 1..12 that do not occur in any of those paths, therefore a(12) = 5.

Prog

(PARI)
up_to = 105;
A332809list(up_to) = { my(v=vector(up_to)); v[1] = Set([1]); for(n=2, up_to, my(f=factor(n)[, 1]~, s=Set([n])); for(i=1, #f, s = setunion(s, v[n-(n/f[i])])); v[n] = s); apply(length, v); }
v332809 = A332809list(up_to);
A332810(n) = (n-v332809[n]);

Crossrefs

Cf. A064097, A332809, A333123.

Sequence in context: A084596 A056641 A010652 * A088752 A239594 A094948

Adjacent sequences: A332807 A332808 A332809 * A332811 A332812 A332813

Keyword

nonn

Author

Antti Karttunen, Apr 04 2020

Status

approved