A376485 Carmichael numbers ordered by largest prime factor, then by size.

561, 1105, 1729, 2465, 2821, 75361, 63973, 1050985, 6601, 41041, 29341, 172081, 552721, 852841, 10877581, 1256855041, 8911, 340561, 15182481601, 72720130561, 10585, 15841, 126217, 825265, 2433601, 496050841, 672389641, 5394826801, 24465723528961, 1074363265, 24172484701, 62745, 2806205689, 22541365441, 46657, 2113921, 6436473121, 6557296321, 13402361281, 26242929505, 65320532641, 143873352001, 105083995864811041

Offset

1,1

Links

Table of n, a(n) for n=1..43.

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)
A376485_list = list(islice(A376485_gen(), 43)) # Chai Wah Wu, Sep 25 2024

Crossrefs

Cf. A002997, A081702, A283715 (row lengths).

Sequence in context: A002997 A355039 A087788 * A173703 A306338 A367320

Adjacent sequences: A376482 A376483 A376484 * A376486 A376487 A376488

Keyword

nonn,tabf

Author

Charles R Greathouse IV, Sep 24 2024

Status

approved