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A111701 Least integer obtained when n is divided by prime(1), then by prime(2), then by prime(3), ..., stopping as soon as one of the primes does not divide it. In particular, a(2n-1) = 2n-1. 19

%I #19 Dec 25 2023 01:51:37

%S 1,1,3,2,5,1,7,4,9,5,11,2,13,7,15,8,17,3,19,10,21,11,23,4,25,13,27,14,

%T 29,1,31,16,33,17,35,6,37,19,39,20,41,7,43,22,45,23,47,8,49,25,51,26,

%U 53,9,55,28,57,29,59,2,61,31,63,32,65,11,67,34,69,35,71,12,73,37,75,38,77

%N Least integer obtained when n is divided by prime(1), then by prime(2), then by prime(3), ..., stopping as soon as one of the primes does not divide it. In particular, a(2n-1) = 2n-1.

%C n divided by the largest primorial that divides it.

%H Amiram Eldar, <a href="/A111701/b111701.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n/A053589(n). - _Amiram Eldar_, Mar 30 2021

%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Sum{k>=1} (1-1/prime(k))/(prime(k-1)#)^2 = 0.68986205818209290747..., where prime(k)# = A002110(k). - _Amiram Eldar_, Dec 25 2023

%t f[n_] := Block[{m = n, k = 1}, While[ IntegerQ[ m/Prime[k]], m = m/Prime[k]; k++ ]; m]; Table[ f[n], {n, 77}] (* _Robert G. Wilson v_, Aug 25 2005 *)

%Y Cf. A002110, A053589, A076934, A114562.

%K easy,nonn

%O 1,3

%A _Amarnath Murthy_, Aug 21 2005

%E More terms from _Robert G. Wilson v_, Aug 25 2005

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)