A064165 -id:A064165 - cp's OEIS frontend

A347718 a(n) = Sum of the divisors of sigma_n(n).

1, 6, 56, 448, 6264, 96348, 1559520, 16908804, 391945400, 20553536052, 706019328000, 20210523379200, 519285252355776, 21710734431216480, 1456143373228677120, 25536237889612326912, 1792353900753729655758, 52839150354952425838080, 4154723599066412190910560

Offset: 1

Wesley Ivan Hurt, Jan 28 2022

nonn

			a(3) = sigma(sigma_3(3)) = sigma(1^3+3^3) = sigma(28) = 1+2+4+7+14+28 = 56.

Daniel Suteu, Table of n, a(n) for n = 1..120 (first 42 terms from Chai Wah Wu)
Index entries for sequences related to sigma(n)

Cf. A000203, A023887, A064165.

a:= n-> (s-> s(s[n](n)))(numtheory[sigma]):
seq(a(n), n=1..20);  # Alois P. Heinz, Jan 28 2022

Table[DivisorSigma[1, DivisorSigma[n, n]], {n, 20}]

from math import prod
from collections import Counter
from sympy import factorint
def A347718(n): return prod((q**(r+1)-1)//(q-1) for q,r in sum((Counter(factorint((p**(n*(e+1))-1)//(p**n-1))) for p, e in factorint(n).items()),Counter()).items()) # Chai Wah Wu, Jan 28 2022

a(n) = sigma(sigma_n(n)).

a(n) = A000203(A023887(n)). - Michel Marcus, Jan 29 2022

A352420 Number of distinct prime factors of sigma_n(n).

Original entry on oeis.org

0, 1, 2, 3, 3, 4, 3, 2, 3, 5, 6, 8, 5, 5, 8, 6, 3, 8, 5, 11, 9, 7, 8, 10, 8, 8, 10, 12, 7, 13, 7, 11, 15, 10, 15, 11, 7, 8, 11, 10, 6, 14, 8, 14, 14, 11, 10, 17, 6, 21, 15, 16, 8, 18, 16, 15, 16, 6, 9, 22, 8, 10, 17, 13, 17, 17, 7, 17, 20, 17, 8, 23, 4, 13, 21

Offset: 1

Wesley Ivan Hurt, Mar 21 2022

nonn

			a(5) = 3; a(5) = omega(sigma_5(5)) = omega(1^5+5^5) = omega(3126) = 3.

Daniel Suteu, Table of n, a(n) for n = 1..120

Cf. A001221 (omega), A023887 (sigma_n(n)).

Cf. A064165, A347718.

A342420 := proc(n)
    A001221(A023887(n)) ; # reuses other codes
end proc:
seq(A342420(n),n=1..20) ; # R. J. Mathar, Apr 06 2022

Table[PrimeNu[DivisorSigma[n, n]], {n, 30}]

a(n) = omega(sigma(n, n)); \\ Daniel Suteu, Mar 23 2022

from sympy import primefactors, factorint
def A352420(n): return len(set().union(*(primefactors((p**((e+1)*n)-1)//(p**n-1)) for p, e in factorint(n).items()))) # Chai Wah Wu, Mar 24 2022

a(n) = omega(sigma_n(n)) = A001221(A023887(n)).

a(67)-a(75) from Daniel Suteu, Mar 23 2022

cp's OEIS Frontend

A347718 a(n) = Sum of the divisors of sigma_n(n).

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