

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.


3



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
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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) = (nv332809[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



