A338160 Number of ways to represent n as a product of the greatest number of distinct factors.

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

Offset

1,12

Comments

a(n) = A058060(n) for 1 < n < 60; a(60) = 3, A058060(60) = 1.

a(n) is the number of factorizations of n into A086435(n) distinct factors > 1.

a(n) depends only on the prime signature of n.

Links

Table of n, a(n) for n=1..96.

Example

a(72) = 3 because 72 = 2*3*12 = 2*4*9 = 3*4*6 and 72 cannot be represented as a product of 4 distinct factors each greater than 1 (adding the factor 1 to each product doesn't change anything).

Prog

(PARI) a(n)={my(d=divisors(n)); my(F(r, k)=if(r==1, [0, 1], my(b=-1, c=0); for(k=2, k, if(r%d[k]==0, my([tb, tc]=self()(r/d[k], k-1)); if(tb>b, b=tb; c=0); if(tb==b, c+=tc))); [b+1, c])); F(n, #d)[2]} \\ Andrew Howroyd, Oct 14 2020

Crossrefs

Cf. A086435, A140207, A338159.

Sequence in context: A348940 A088530 A058060 * A336137 A371735 A088323

Adjacent sequences: A338157 A338158 A338159 * A338161 A338162 A338163

Keyword

nonn

Author

Vladimir Letsko, Oct 14 2020

Extensions

More terms from Andrew Howroyd, Oct 14 2020

Status

approved