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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
OFFSET
1,2
LINKS
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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 07 2017
STATUS
approved