A276151 n minus the greatest primorial number (A002110) which divides n: a(n) = n - A053589(n).

0, 0, 2, 2, 4, 0, 6, 6, 8, 8, 10, 6, 12, 12, 14, 14, 16, 12, 18, 18, 20, 20, 22, 18, 24, 24, 26, 26, 28, 0, 30, 30, 32, 32, 34, 30, 36, 36, 38, 38, 40, 36, 42, 42, 44, 44, 46, 42, 48, 48, 50, 50, 52, 48, 54, 54, 56, 56, 58, 30, 60, 60, 62, 62, 64, 60, 66, 66, 68, 68, 70, 66, 72, 72, 74, 74, 76, 72, 78, 78, 80, 80, 82, 78, 84, 84, 86, 86, 88, 60, 90, 90, 92

Offset: 1

Author

Antti Karttunen, Aug 23 2016

Keywords

• nonn

Comments

Subtract one (in primorial base representation A049345) from the least significant nonzero digit of n, then convert back to decimal.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2310
• Index entries for sequences related to primorial base

Crossrefs

Cf. A002110 (positions of zeros), A032742, A049345, A053589, A111701, A276084, A276085, A276086.

Programs

Mathematica

Table[If[n == 1, 0, n - Times @@ Prime@ Flatten@ Position[TakeWhile[#, # > 0 &], 1] &@ Function[f, ReplacePart[Table[0, {PrimePi[f[[-1, 1]]]}], #] &@ Map[PrimePi@ First@ # -> 1 &, f]]@ FactorInteger@ n], {n, 93}] (* or *)
Table[n - If[OddQ@ n, 1, Function[p, Product[Prime@ k, {k, #[[p]]}]][LengthWhile[Differences@ #, # == 1 &] + 1] &@ PrimePi[FactorInteger[n][[All, 1]]]], {n, 93}] (* Michael De Vlieger, Aug 26 2016 *)

Python

from sympy import nextprime, primepi, primorial
def a002110(n): return 1 if n<1 else primorial(n)
def a053669(n):
    p = 2
    while True:
        if n%p!=0: return p
        else: p=nextprime(p)
def a276084(n): return primepi(a053669(n)) - 1
def a(n): return n - a002110(a276084(n))
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 23 2017

Scheme

(define (A276151 n) (- n (A053589 n)))

Formula

a(n) = n - A053589(n) = n - A002110(A276084(n)).

a(n) = A276085(A032742(A276086(n))). - Antti Karttunen, May 11 2017