A340592 a(n) is the concatenation of the prime factors (with multiplicity) of n mod n.

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

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

Robert Israel, Table of n, a(n) for n = 2..10000

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

Cf. A037276, A340594, A340595.

Sequence in context: A329375 A078153 A104035 * A326831 A196409 A369909

Adjacent sequences: A340589 A340590 A340591 * A340593 A340594 A340595

Keyword

nonn,base

Author

J. M. Bergot and Robert Israel, Jan 12 2021

Status

approved