A243915 a(n) = sigma(omega(n)).

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

Offset: 2

Author

Wesley Ivan Hurt, Jun 14 2014

Keywords

• nonn
• easy

Comments

If n is the product of k distinct primes, then a(n) = sigma(k).

Records occur at n = 2, 6, 30, 210, 30030, ... . - R. J. Mathar, Jun 18 2014 [The position of the n-th record is A002110(A002093(n)). - Amiram Eldar, Dec 29 2024]

If n = p^k where p is prime and k is a positive integer, a(p^k) = sigma(omega(p^k)) = sigma(1) = 1. - Wesley Ivan Hurt, May 21 2021

Links

• G. C. Greubel, Table of n, a(n) for n = 2..5000

Crossrefs

Cf. A000203 (sigma), A001221 (omega), A002110, A002093.

Programs

Maple

with(numtheory):
A243915 := proc(n)
    sigma(nops(factorset(n))) ;
end proc:
seq(A243915(n), n=2..100); # R. J. Mathar, Jun 18 2014

Mathematica

Table[DivisorSigma[1, PrimeNu[n]], {n, 2, 100}]

PARI

for(n=2,50, print1(sigma(omega(n)), ", ")) \\ G. C. Greubel, May 17 2017

Formula

a(n) = A000203(A001221(n)).