A324869 a(n) is the number of times A324862(d) attains the maximal value it obtains among the divisors d of n.

1, 2, 2, 1, 2, 1, 2, 1, 1, 4, 2, 3, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 3, 3, 1, 1, 3, 2, 2, 2, 2, 4, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 3, 2, 1, 2, 2, 3, 6, 1, 3, 2, 2, 1, 3, 1, 1, 2, 2, 2, 1, 2, 1, 4, 3, 2, 3, 4, 2, 2, 1, 2, 1, 1, 3, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 3, 2, 1, 1, 3, 4, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 3, 1

Offset: 1

Author

Antti Karttunen, Mar 21 2019

Keywords

• nonn

Examples

			Divisors of 9 are [1, 3, 4]. A324862 applied to these gives values [0, 0, 3], of which the largest (3) occurs just once, thus a(9) = 1.
Divisors of 10 are [1, 2, 5, 10]. A324862 applied to these gives values [0, 0, 0, 0], of which the largest (0) occurs just four times, thus a(10) = 4.
Divisors of 88 are [1, 2, 4, 8, 11, 22, 44, 88]. A324862 applied to these gives values [0, 0, 1, 0, 0, 1, 1, 0], of which the largest (which is 1) occurs three times, thus a(88) = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A324862, A324864.

Programs

PARI

A324869(n) = { my(m=0,w,c=0); fordiv(n,d,w=A324862(d); if(w>=m,if(w==m,c++,c=1;m=w))); (c); };

Formula

a(n) = Sum_{d|n} [A324862(d) = A324864(n)], where [ ] is the Iverson bracket.

a(p) = 2 for all primes p.