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A165725 Largest divisor of n coprime to 30. I.e., a(n) = max { k | gcd(n, k) = k and gcd(k, 30) = 1 }. 2
1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 11, 1, 13, 7, 1, 1, 17, 1, 19, 1, 7, 11, 23, 1, 1, 13, 1, 7, 29, 1, 31, 1, 11, 17, 7, 1, 37, 19, 13, 1, 41, 7, 43, 11, 1, 23, 47, 1, 49, 1, 17, 13, 53, 1, 11, 7, 19, 29, 59, 1, 61, 31, 7, 1, 13, 11, 67, 17, 23, 7, 71, 1, 73, 37, 1, 19, 77, 13, 79, 1, 1, 41, 83, 7 (list; graph; refs; listen; history; text; internal format)
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

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.

PROG

(PARI) a(n)=n>>valuation(n, 2)/3^valuation(n, 3)/5^valuation(n, 5) \\ Charles R Greathouse IV, Jul 16 2017

CROSSREFS

A051037 gives the smooth five numbers, numbers whose prime divisor only include 2, 3 and 5. A132740 gives the largest divisor of n coprime to 10. A065330 gives a(n) = max { k | gcd(n, k) = k and gcd(k, 6) = 1 }.

Largest divisor of n coprime to a prime factor of 30: A000265 (2), A038502 (3), A132739 (5).

Sequence in context: A317940 A318674 A284118 * A214685 A327670 A178637

Adjacent sequences:  A165722 A165723 A165724 * A165726 A165727 A165728

KEYWORD

mult,nonn,easy

AUTHOR

Barry Wells (wells.barry(AT)gmail.com), Sep 25 2009

STATUS

approved

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Last modified April 18 07:59 EDT 2021. Contains 343084 sequences. (Running on oeis4.)