A276094 a(n) = n modulo A002110(A257993(n)), a(0) = 0.

0, 1, 2, 1, 4, 1, 6, 1, 2, 1, 4, 1, 12, 1, 2, 1, 4, 1, 18, 1, 2, 1, 4, 1, 24, 1, 2, 1, 4, 1, 30, 1, 2, 1, 4, 1, 6, 1, 2, 1, 4, 1, 12, 1, 2, 1, 4, 1, 18, 1, 2, 1, 4, 1, 24, 1, 2, 1, 4, 1, 60, 1, 2, 1, 4, 1, 6, 1, 2, 1, 4, 1, 12, 1, 2, 1, 4, 1, 18, 1, 2, 1, 4, 1, 24, 1, 2, 1, 4, 1, 90, 1, 2, 1, 4, 1, 6, 1, 2, 1, 4, 1, 12, 1, 2, 1, 4, 1, 18, 1

Offset: 0

Author

Antti Karttunen, Aug 22 2016

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..2310

Crossrefs

Cf. A000040, A002110, A257993, A276084, A276088, A276093.

Programs

Mathematica

{0}~Join~Table[k = 1; While[! CoprimeQ[Prime@ k, n], k++]; Mod[n, Product[Prime@ i, {i, k}]], {n, 79}] (* Michael De Vlieger, Jun 22 2017 *)

Python

from sympy import nextprime, primepi, primorial
def a053669(n):
    p = 2
    while True:
        if n%p: return p
        else: p=nextprime(p)
def a257993(n): return primepi(a053669(n))
def a002110(n): return 1 if n<1 else primorial(n)
def a(n): return 0 if n==0 else n%a002110(a257993(n))
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 22 2017

Formula

a(0) = 0, and for n >= 1, a(n) = n modulo A002110(A257993(n)).

or a(n) = A276088(n) * A002110(A276084(n)).

Other identities. For all n >= 0:

a(n) = n - A276093(n).