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A280684 a(n) = number of divisors of the product of the divisors of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 24 04:25 EDT 2019. Contains 323528 sequences. (Running on oeis4.)