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

1,1

Links

Table of n, a(n) for n=1..7.

Example

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.

Prog

(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

Crossrefs

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

Subsequence of A037020.

Sequence in context: A068556 A078243 A024246 * A024247 A067445 A167003

Adjacent sequences: A358196 A358197 A358198 * A358200 A358201 A358202

Keyword

nonn,more

Author

Jean-Marc Rebert, Nov 02 2022

Status

approved