A358890 -id:A358890 - cp's OEIS frontend

A079749 Erroneous version of A358890.

3, 2, 1, 8, 90, 168, 9352, 46189, 2515371, 721970, 6449639, 565062156, 11336460025, 37151747513, 256994754033

Offset: 1

dead

Name was: "Consider the first occurrence of a run of exactly n successive numbers whose greatest prime factors are monotonically increasing; a(n) is the first of these n numbers."

It seems unclear whether the run of n successive numbers mentioned in the name is allowed to be extendable to the left or not. In other words, is a(n) the smallest number m >= 1 in a run of n consecutive numbers (m, m+1, ..., m+n-1), (A) such that gpf(m) < gpf(m+1) < ... < gpf(m+n-1) > gpf(m+n), or (B) such that gpf(m-1) > gpf(m) (or m = 1) and gpf(m) < gpf(m+1) < ... < gpf(m+n-1) > gpf(m+n)? (Here, gpf(k) = A006530(k), the greatest prime factor of k, with the convention gpf(1) = 1.) In both cases, at least one term is incorrect: in case (A), a(9) should be 721971; in case (B), a(1) should be 14 and a(2) should be 4. - Pontus von Brömssen, Nov 07 2022

A079866 a(1)=1 and for n>1: floor(n^(1/Omega(n))), where Omega(n) is the total number of prime factors of n (A001222).

Original entry on oeis.org

1, 2, 3, 2, 5, 2, 7, 2, 3, 3, 11, 2, 13, 3, 3, 2, 17, 2, 19, 2, 4, 4, 23, 2, 5, 5, 3, 3, 29, 3, 31, 2, 5, 5, 5, 2, 37, 6, 6, 2, 41, 3, 43, 3, 3, 6, 47, 2, 7, 3, 7, 3, 53, 2, 7, 2, 7, 7, 59, 2, 61, 7, 3, 2, 8, 4, 67, 4, 8, 4, 71, 2, 73, 8, 4, 4, 8, 4, 79, 2, 3, 9, 83, 3, 9, 9, 9, 3, 89, 3, 9, 4, 9, 9, 9, 2

Offset: 1

Reinhard Zumkeller, Jan 13 2003

nonn

a(n) <= A079868(n).
A020639(n) <= a(n) <= A006530(n);
a(m) = A079868(m) = A079870(m) iff m is a prime power (A000961).

David W. Wilson, Table of n, a(n) for n = 1..10000

A079867(n) = a(n)^A001222(n).

Cf. A079747, A358890.

A079866 := proc(n)
    root[numtheory[bigomega](n)](n) ;
    floor(%) ;
end proc:
seq(A079866(n),n=1..97) ; # R. J. Mathar, Sep 07 2016

Join[{1}, Table[Floor[n^(1/PrimeOmega[n])], {n, 2, 20}]] (* G. C. Greubel, Sep 16 2016 *)

a(n) = if (n==1, 1, sqrtnint(n, bigomega(n))); \\ Michel Marcus, Sep 09 2016

A100384 a(n) = the smallest number x >= 2 such that for m = x to x + n - 1, A006530(m) increases.

Original entry on oeis.org

2, 2, 8, 8, 90, 168, 9352, 46189, 721970, 721970, 6449639, 565062156, 11336460025, 37151747513, 256994754033

Offset: 1

Labos Elemer, Dec 09 2004

A006530(m) is the largest prime factor of m.
a(16) > 3*10^11. - Donovan Johnson, Oct 24 2009
a(16) > 10^13. - Giovanni Resta, Jul 25 2013

			a(5)=90 because the largest prime factors of 90,91,92,93,94 are 5,13,23,31,47.

Cf. A006530, A070089, A071869, A100376, A100385, A358890.

from sympy import factorint
def A100384(n):
    k, a = 2, [max(factorint(m+2)) for m in range(n)]
    while True:
        for i in range(1, n):
            if a[i-1] >= a[i]:
                break
        else:
            return k
        a = a[i:] + [max(factorint(k+j+n)) for j in range(i)]
        k += i # Chai Wah Wu, Jul 24 2017

Edited by Don Reble, Jun 13 2007
a(13)-a(15) from Donovan Johnson, Oct 24 2009
Name clarified by Peter Munn, Dec 05 2022

A079748 Largest k such that the greatest prime factors from n to n+k are monotonically increasing.

Original entry on oeis.org

2, 1, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 2, 1, 0, 2, 1, 0, 1, 0, 2, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 2, 1, 0, 0, 2, 1, 0, 2, 1, 0, 0, 1, 0, 4, 3, 2, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2

Offset: 1

Reinhard Zumkeller, Jan 10 2003

nonn

A006530(n+i) < A006530(n+j) for 0 <= i < j < a(n);

if a(n) > 0 then a(n+1) = a(n) - 1.

			n=20: 20 = 5*2^2, 21 = 7*3, 22 = 11*2 and 23, followed by 24 = 3*2^3: therefore a(20)=3 (5 < 7 < 11 < 23 and 23 > 3).

Cf. A006530, A070087, A079747, A358890.

a(n) = 0 if and only if n is a term of A070087. - Pontus von Brömssen, Nov 09 2022

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A079749 Erroneous version of A358890.

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A079866 a(1)=1 and for n>1: floor(n^(1/Omega(n))), where Omega(n) is the total number of prime factors of n (A001222).

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A100384 a(n) = the smallest number x >= 2 such that for m = x to x + n - 1, A006530(m) increases.

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A079748 Largest k such that the greatest prime factors from n to n+k are monotonically increasing.

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