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

1,2

Links

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

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.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A103178 A173300 A181236 * A322671 A087909 A076078

Adjacent sequences: A280681 A280682 A280683 * A280685 A280686 A280687

Keyword

nonn

Author

Jaroslav Krizek, Jan 07 2017

Status

approved