OFFSET
1,2
COMMENTS
Numbers k such that the concatenation of prime factors of k is 1 less than a multiple of k.
Contains 2*m for m in A093170.
Terms k where k-1 is prime include 6, 14, 18, 48 and 284. Are there others?
LINKS
Martin Ehrenstein, Table of n, a(n) for n = 1..38
EXAMPLE
a(4) = 48 is a term because 48=2*2*2*2*3 and 22223 == -1 (mod 48).
MAPLE
tcat:= proc(x, y) x*10^(1+ilog10(y))+y end proc:
filter:= proc(n) local F, t, i;
F:= map(t -> t[1]$t[2], sort(ifactors(n)[2], (a, b)->a[1]<b[1]));
t:= F[1];
for i from 2 to nops(F) do
t:= tcat(t, F[i])
od;
t mod n = n-1
end proc:
filter(1):= true:
select(filter, [$1..10^8]);
PROG
(Python)
from sympy import factorint
def A037276(n):
if n == 1: return 1
return int("".join(str(p)*e for p, e in sorted(factorint(n).items())))
def afind(limit, startk=1):
for k in range(startk, limit+1):
if (A037276(k) + 1)%k == 0:
print(k, end=", ")
afind(10**6) # Michael S. Branicky, Feb 27 2022
# adapted and corrected by Martin Ehrenstein, Mar 06 2022
(Python)
from itertools import count, islice
from sympy import factorint
def A351975_gen(startvalue=1): # generator of terms >= startvalue
for k in count(max(startvalue, 1)):
c = 0
for d in sorted(factorint(k, multiple=True)):
c = (c*10**len(str(d)) + d) % k
if c == k-1:
yield k
CROSSREFS
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, Feb 26 2022
EXTENSIONS
a(24)-a(25) from Michael S. Branicky, Feb 27 2022
Prepended 1 and more terms from Martin Ehrenstein, Feb 28 2022
STATUS
approved