A366757 -id:A366757 - cp's OEIS frontend

A366758 a(n) is the sum of the divisors of n!+1.

3, 3, 4, 8, 31, 133, 832, 5113, 41044, 388800, 3958704, 39916802, 518682390, 6302045232, 90968651712, 1332614649600, 22844265373440, 356226551466344, 7504470340300800, 123358411682195904, 2432902126073962432, 52279222588118377280, 1175121515279802150144

Offset: 0

Sean A. Irvine, Oct 20 2023

nonn

			a(5) = 133 because the divisors of 5!+1 are {1, 11, 121}.

Cf. A038507, A000203, A064144, A062569, A366757.

a:=n->numtheory[sigma](n!+1):
seq(a(n), n=0..30);

DivisorSigma[1,Range[0,25]!+1] (* Paolo Xausa, Oct 21 2023 *)

from math import factorial
from sympy import divisor_sigma
def A366758(n): return divisor_sigma(factorial(n)+1) # Chai Wah Wu, Oct 20 2023

a(n) = sigma(n!+1) = A000203(A038507(n)).

A366812 The sum of the divisors of prime(n)#+1 where p# is the product of all the primes from 2 to p inclusive.

Original entry on oeis.org

3, 4, 8, 32, 212, 2312, 30600, 544880, 9727992, 223796952, 6500793728, 200560490132, 7461870828048, 309238687200848, 13161101219883792, 615548170519961184, 33465582319854797280, 1930276657976815787040, 117814338226489513454272, 7858321551223903311137992

Offset: 0

Sean A. Irvine, Oct 23 2023

nonn

			a(6) = 30600 because the divisors of 13#+1 = 30031 are {1, 59, 509, 30031}.

Amiram Eldar, Table of n, a(n) for n = 0..98

Cf. A006862, A000230, A054988, A366809, A366811, A366757.

seq(numtheory[sigma](mul(ithprime(k), k=1..n)-1), n=0..30);

Map[DivisorSigma[1, #] &, 1 + FoldList[Times, 1, Prime@ Range@ 19] ] (* Michael De Vlieger, Oct 25 2023 *)

a(n) = sigma(prime(n)#+1) = A000230(A006862(n)).

cp's OEIS Frontend

A366758 a(n) is the sum of the divisors of n!+1.

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