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A340592 a(n) is the concatenation of the prime factors (with multiplicity) of n mod n. 5
0, 0, 2, 0, 5, 0, 6, 6, 5, 0, 7, 0, 13, 5, 14, 0, 17, 0, 5, 16, 13, 0, 15, 5, 5, 9, 3, 0, 25, 0, 14, 14, 13, 22, 1, 0, 29, 1, 25, 0, 27, 0, 11, 20, 39, 0, 47, 28, 5, 11, 29, 0, 11, 16, 43, 34, 55, 0, 15, 0, 45, 22, 14, 58, 1, 0, 41, 47, 47, 0, 57, 0, 15, 55, 15, 18, 51, 0, 65, 12, 77, 0, 53, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,3
COMMENTS
a(n) = 0 if n is prime.
The first composite n for which a(n)=0 is 28749. Are there others?
There are no other composite n terms for which a(n)=0 up to 5 million. - Harvey P. Dale, Jul 17 2023
LINKS
FORMULA
a(n) = A037276(n) mod n.
EXAMPLE
For n = 20 = 2*2*5, a(20) = 225 mod 20 = 5.
MAPLE
dcat:= proc(L) local i, x;
x:= L[-1];
for i from nops(L)-1 to 1 by -1 do
x:= 10^(1+ilog10(x))*L[i]+x
od;
x
end proc:
f:= proc(n) local F;
F:= sort(ifactors(n)[2], (a, b) -> a[1] < b[1]);
dcat(map(t -> t[1]$t[2], F)) mod n;
end proc:
map(f, [$2..100]);
MATHEMATICA
Table[Mod[FromDigits[Flatten[IntegerDigits/@Table[#[[1]], #[[2]]]&/@FactorInteger[n]]], n], {n, 2, 100}] (* Harvey P. Dale, Jul 17 2023 *)
PROG
(Python)
from sympy import factorint
def a(n):
if n == 1: return 0
return int("".join(str(f) for f in factorint(n, multiple=True)))%n
print([a(n) for n in range(2, 86)]) # Michael S. Branicky, Jan 18 2022
CROSSREFS
Sequence in context: A329375 A078153 A104035 * A326831 A196409 A369909
KEYWORD
nonn,base
AUTHOR
J. M. Bergot and Robert Israel, Jan 12 2021
STATUS
approved

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Last modified February 28 08:11 EST 2024. Contains 370393 sequences. (Running on oeis4.)