OFFSET
1,1
EXAMPLE
17: 561, 1105;
19: 1729;
23:
29: 2465;
31: 2821, 75361;
37: 63973, 1050985;
41: 6601, 41041;
43:
47:
53:
59:
61: 29341, 172081, 552721, 852841, 10877581, 1256855041;
67: 8911, 340561, 15182481601;
71: 72720130561;
73: 10585, 15841, 126217, 825265, 2433601, 496050841, 672389641, 5394826801, 24465723528961;
79: 1074363265, 24172484701
83:
89: 62745, 2806205689, 22541365441;
97: 46657, 2113921, 6436473121, 6557296321, 13402361281, 26242929505, 65320532641, 143873352001, 105083995864811041
101: 101101, 252601, 2100901, 9494101, 6820479601, 109038862801, 102967089120001
PROG
(PARI) \\ This program is inefficient and functions as proof-of-concept only.
Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
car(n)=n%2 && !isprime(n) && Korselt(n) && n>1
row(k)=my(p=prime(k)); fordiv(prod(i=2, k-1, prime(i)), n, if(car(p*n), print1(p*n, ", ")))
(Python)
from itertools import islice, combinations
from math import prod
from sympy import nextprime
def A376485_gen(): # generator of terms
plist, p = [3, 5], 7
while True:
clist = []
for l in range(2, len(plist)+1):
for q in combinations(plist, l):
k = prod(q)*p-1
if not (k%(p-1) or any(k%(r-1) for r in q)):
clist.append(k+1)
yield from sorted(clist)
plist.append(p)
p = nextprime(p)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Charles R Greathouse IV, Sep 24 2024
STATUS
approved