A373382 - OEIS

A373382

a(n) = gcd(A329697(n), A331410(n)), where A329697, A331410 give the number of iterations needed to reach a power of 2, when using the map n -> n-(n/p), or respectively, n -> n+(n/p), where p is the largest prime factor of n.

0, 0, 1, 0, 1, 1, 1, 0, 2, 1, 2, 1, 2, 1, 1, 0, 1, 2, 3, 1, 1, 2, 1, 1, 2, 2, 3, 1, 1, 1, 1, 0, 3, 1, 3, 2, 1, 3, 3, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 1, 3, 1, 1, 4, 1, 4, 1, 1, 1, 1, 0, 1, 3, 4, 1, 1, 3, 1, 2, 1, 1, 1, 3, 1, 3, 1, 1, 4, 1, 3, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 4, 2, 1, 2, 3, 2, 4

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OFFSET

1,9

COMMENTS

As A329697 and A331410 are both fully additive sequences, all sequences that give the positions of multiples of some natural number k in this sequence are closed under multiplication, i.e., are multiplicative semigroups.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

FORMULA

a(n) = gcd(A329697(n), A334861(n)) = gcd(A331410(n), A334861(n)).

a(n) = gcd(A329697(n), A335877(n)) = gcd(A331410(n), A335877(n)).

PROG

(PARI)

A329697(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(1+A329697(f[k, 1]-1)))); };

A331410(n) = { my(f=factor(n)); sum(k=1, #f~, if(2==f[k, 1], 0, f[k, 2]*(1+A331410(f[k, 1]+1)))); };

A373382(n) = gcd(A329697(n), A331410(n));

CROSSREFS

Cf. A329697, A331410, A334861, A335877.