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

1,3

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

Formula

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

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A061006 A080736 A326127 * A144412 A360603 A337299

Adjacent sequences: A276148 A276149 A276150 * A276152 A276153 A276154

Keyword

nonn

Author

Antti Karttunen, Aug 23 2016

Status

approved