A280684 a(n) = number of divisors of the product of the divisors of n.

1, 2, 2, 4, 2, 9, 2, 7, 4, 9, 2, 28, 2, 9, 9, 11, 2, 28, 2, 28, 9, 9, 2, 65, 4, 9, 7, 28, 2, 125, 2, 16, 9, 9, 9, 100, 2, 9, 9, 65, 2, 125, 2, 28, 28, 9, 2, 126, 4, 28, 9, 28, 2, 65, 9, 65, 9, 9, 2, 637, 2, 9, 28, 22, 9, 125, 2, 28, 9, 125, 2, 247, 2, 9, 28

Offset: 1

Author

Jaroslav Krizek, Jan 07 2017

Keywords

• nonn

Examples

			For n = 4; a(n) = tau (1*2*4) = tau(8) = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000040, A001248, A007955, A008578, A052213, A280685, A280582.

Programs

Magma

[#[d: d in Divisors(&*[d: d in Divisors(n)])]: n in [1..100]]

PARI

A007955(n) = if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2)); \\ This function from Charles R Greathouse IV, Feb 11 2011
A280684(n) = numdiv(A007955(n)); \\ Antti Karttunen, May 19 2017

Formula

a(n) = A000005(A007955(n)).

a(p) = 2 for p = primes (A000040).

a(n) = 4 for squares of primes (A001248).

a(n) = n for numbers 1, 2, 4, 28, 100, ...

a(n) = tau(n) for noncomposites (A008578).

a(n) = a(n+1) for numbers in A052213.