A358199 a(n) is the least integer whose sum of the i-th powers of the proper divisors is a prime for 1 <= i <= n, or -1 if no such number exists.

4, 4, 981, 8829, 8829, 122029105, 2282761881

Offset: 1

Author

Jean-Marc Rebert, Nov 02 2022

Keywords

• nonn
• more

Examples

			4 is a term since the strict divisors of 4 are {1, 2}, 1^1 + 2^1 = 3 and 1^2 + 2^2 = 5 are prime and no number < 4 has this property.
		

Crossrefs

Cf. A001065 (s1), A180852, A357324, A057709, A000203, A001157, A001158.

Subsequence of A037020.

Programs

PARI

card(n)=my(c=1,s=0);s=sigma(n)-n;while(isprime(s),c++;s=sigma(n,c)-n^c);c--
a(n)=my(x=0);for(k=1,+oo,x=card(k);if(x>=n,return(k)))

Python

from itertools import count
from math import prod
from sympy import isprime, factorint
def A358199(n):
    for m in count(2):
        f = factorint(m).items()
        if all(map(isprime,(prod((p**((e+1)*i)-1)//(p**i-1) for p,e in f) - m**i for i in range(1,n+1)))):
            return m # Chai Wah Wu, Nov 15 2022