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%I #24 Mar 18 2021 11:17:29
%S 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,
%T 26,26,28,0,30,30,32,32,34,30,36,36,38,38,40,36,42,42,44,44,46,42,48,
%U 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
%N n minus the greatest primorial number (A002110) which divides n: a(n) = n - A053589(n).
%C Subtract one (in primorial base representation A049345) from the least significant nonzero digit of n, then convert back to decimal.
%H Antti Karttunen, <a href="/A276151/b276151.txt">Table of n, a(n) for n = 1..2310</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F a(n) = n - A053589(n) = n - A002110(A276084(n)).
%F a(n) = A276085(A032742(A276086(n))). - _Antti Karttunen_, May 11 2017
%t 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 *)
%t 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 *)
%o (Scheme) (define (A276151 n) (- n (A053589 n)))
%o (Python)
%o from sympy import nextprime, primepi, primorial
%o def a002110(n): return 1 if n<1 else primorial(n)
%o def a053669(n):
%o p = 2
%o while True:
%o if n%p!=0: return p
%o else: p=nextprime(p)
%o def a276084(n): return primepi(a053669(n)) - 1
%o def a(n): return n - a002110(a276084(n))
%o print([a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Jun 23 2017
%Y Cf. A002110 (positions of zeros), A032742, A049345, A053589, A111701, A276084, A276085, A276086.
%K nonn
%O 1,3
%A _Antti Karttunen_, Aug 23 2016
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