A358199 - OEIS

%I #30 Nov 16 2022 06:58:01

%S 4,4,981,8829,8829,122029105,2282761881

%N 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.

%e 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.

%o (PARI)

%o card(n)=my(c=1,s=0);s=sigma(n)-n;while(isprime(s),c++;s=sigma(n,c)-n^c);c--

%o a(n)=my(x=0);for(k=1,+oo,x=card(k);if(x>=n,return(k)))

%o (Python)

%o from itertools import count

%o from math import prod

%o from sympy import isprime, factorint

%o def A358199(n):

%o     for m in count(2):

%o         f = factorint(m).items()

%o         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)))):

%o             return m # _Chai Wah Wu_, Nov 15 2022

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

%Y Subsequence of A037020.

%K nonn,more

%O 1,1

%A _Jean-Marc Rebert_, Nov 02 2022