OFFSET
1,7
COMMENTS
This is the sequence of the largest divisor of n which is coprime to 30. The product of the first 3 prime numbers is 2*3*5=30. This sequence gives the largest factor of n which does not include 2, 3 or 5 in its prime factorization.
LINKS
Barry Wells, Table of n, a(n) for n = 1..1024 [a(392) and a(704) corrected by Sean A. Irvine]
FORMULA
From Amiram Eldar, Jul 10 2022: (Start)
Multiplicative with a(p^e) = p^e if p >= 7 and 1 otherwise.
a(n) = n/A355582(n). (End)
Sum_{k=1..n} a(k) ~ (5/24) * n^2. - Amiram Eldar, Nov 28 2022
Dirichlet g.f.: zeta(s-1)*(2^s-2)*(3^s-3)*(5^s-5)/((2^s-1)*(3^s-1)*(5^s-1)). - Amiram Eldar, Jan 04 2023
EXAMPLE
The largest factor of 1, 2, 3, 4, 5 and 6 not including the primes 2, 3 and 5 is 1. 7 is prime and therefore its sequence value is 7. For p > 5, p prime, gives a(p) = p. As 14 = 2*7, a(14)= 7. As 98 = 2*7*7, a(98)= 49.
MATHEMATICA
a[n_] := n / Times @@ ({2, 3, 5}^IntegerExponent[n, {2, 3, 5}]); Array[a, 100] (* Amiram Eldar, Jul 10 2022 *)
PROG
(PARI) a(n)=n>>valuation(n, 2)/3^valuation(n, 3)/5^valuation(n, 5) \\ Charles R Greathouse IV, Jul 16 2017
CROSSREFS
KEYWORD
mult,nonn,easy
AUTHOR
Barry Wells (wells.barry(AT)gmail.com), Sep 25 2009
STATUS
approved