A366386 Excess of n when n is factored into factors q(i) = prime(i)/i: a(n) = A196050(n) - A324923(n).

0, 0, 0, 1, 0, 1, 1, 2, 2, 1, 0, 2, 1, 2, 2, 3, 1, 3, 2, 2, 2, 1, 2, 3, 3, 2, 4, 3, 1, 3, 0, 4, 2, 2, 2, 4, 2, 3, 3, 3, 1, 3, 2, 2, 4, 3, 2, 4, 4, 4, 2, 3, 3, 5, 3, 4, 3, 2, 1, 4, 3, 1, 4, 5, 3, 3, 2, 3, 4, 3, 2, 5, 2, 3, 5, 4, 2, 4, 1, 4, 6, 2, 2, 4, 2, 3, 3, 3, 3, 5, 3, 4, 2, 3, 3, 5, 3, 5, 4, 5, 2, 3, 4, 4, 4, 4, 3, 6

Offset: 1

Author

Antti Karttunen, Oct 23 2023

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to Matula-Goebel numbers
• Index entries for sequences related to prime indices in the factorization of n

Crossrefs

Cf. A006530, A196050, A324923.

Cf. A007097 (positions of 0's), A358731 (of 1's).

Cf. also A046660, A358729.

Programs

PARI

A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
A366386(n) = { my(lista = List([]), gpf, i); while(n > 1, gpf=A006530(n); i = primepi(gpf); n /= gpf; n *= i; listput(lista,i)); #lista - #Set(lista); };

Formula

a(n) = A196050(n) - A324923(n).

a(n) <= A358729(n).