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.

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

Offset: 1

Author

Amarnath Murthy, Aug 21 2005

Keywords

• easy
• nonn

Comments

n divided by the largest primorial that divides it.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A053589, A076934, A114562.

Programs

Mathematica

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 *)

Formula

a(n) = n/A053589(n). - Amiram Eldar, Mar 30 2021

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

Extensions

More terms from Robert G. Wilson v, Aug 25 2005