

A248577


Product of the number of divisors of n and the number of distinct prime divisors of n; i.e., tau(n) * omega(n).


4



0, 2, 2, 3, 2, 8, 2, 4, 3, 8, 2, 12, 2, 8, 8, 5, 2, 12, 2, 12, 8, 8, 2, 16, 3, 8, 4, 12, 2, 24, 2, 6, 8, 8, 8, 18, 2, 8, 8, 16, 2, 24, 2, 12, 12, 8, 2, 20, 3, 12, 8, 12, 2, 16, 8, 16, 8, 8, 2, 36, 2, 8, 12, 7, 8, 24, 2, 12, 8, 24, 2, 24, 2, 8, 12, 12, 8, 24
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OFFSET

1,2


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000


FORMULA

a(n) = A000005(n) * A001221(n).
If n is squarefree, then a(n) = omega(n)*2^omega(n).  Wesley Ivan Hurt, Jun 09 2020


EXAMPLE

a(6) = 8; 6 has four divisors {1,2,3,6} and two distinct prime divisors {2,3}, so a(6) = 4*2 = 8.
a(9) = 3; 9 has three divisors {1,3,9} and 1 distinct prime divisor {3}, so a(9) = 3*1 = 3.
a(12) = 12; 12 has 6 divisors {1,2,3,4,6,12} and 2 distinct prime divisors {2,3}, so a(12) = 6*2 = 12.


MAPLE

with(numtheory): A248577:=n>tau(n)*nops(factorset(n)): seq(A248577(n), n=1..100);


MATHEMATICA

Table[DivisorSigma[0, n] PrimeNu[n], {n, 100}]


PROG

(PARI) vector(100, n, numdiv(n)*omega(n)) \\ Michel Marcus, Oct 09 2014


CROSSREFS

Cf. A000005 (tau), A001221 (omega).
Sequence in context: A244080 A141652 A117754 * A015999 A225244 A345281
Adjacent sequences: A248574 A248575 A248576 * A248578 A248579 A248580


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Oct 08 2014


STATUS

approved



