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A079277 Largest integer k < n such that any prime factor of k is also a prime factor of n. 3
1, 1, 2, 1, 4, 1, 4, 3, 8, 1, 9, 1, 8, 9, 8, 1, 16, 1, 16, 9, 16, 1, 18, 5, 16, 9, 16, 1, 27, 1, 16, 27, 32, 25, 32, 1, 32, 27, 32, 1, 36, 1, 32, 27, 32, 1, 36, 7, 40, 27, 32, 1, 48, 25, 49, 27, 32, 1, 54, 1, 32, 49, 32, 25, 64, 1, 64, 27, 64, 1, 64, 1, 64, 45, 64, 49, 72, 1, 64, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

The function a(n) complements Euler's phi-function: 1) a(n)+phi(n)=n if n is a power of a prime. 2) It seems also that a(n)+phi(n)>=n for "almost all numbers". 3) a(2n)=n+1 if and only if n is a Mersenne prime. 4) Lim a(n^k)/n^k =1 if n has at least two prime factors and k goes to infinity.

LINKS

David W. Wilson, Table of n, a(n) for n = 2..10000

FORMULA

Largest k < n with rad(kn) = rad(n), where rad = A007947.

EXAMPLE

a(10)=8 since 8 is the largest integer< 10 that can be written using only the primes 2 and 5. a(78)=72 since 72 is the largest number less than 78 that can be written using only the primes 2, 3 and 13. (78=2*3*13).

PROG

(PARI) a(n) = {forstep(k = n - 1, 2, -1, f = factor(k); okk = 1; for (i=1, #f~, if ((n % f[i, 1]) != 0, okk = 0; break; )); if (okk, return (k)); ); return (1); } \\ Michel Marcus, Jun 11 2013

CROSSREFS

Sequence in context: A024994 A243329 A051953 * A066452 A007104 A102627

Adjacent sequences:  A079274 A079275 A079276 * A079278 A079279 A079280

KEYWORD

nonn

AUTHOR

Istvan Beck (istbe(AT)online.no), Feb 07 2003

STATUS

approved

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Last modified March 23 20:15 EDT 2017. Contains 283957 sequences.