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A137795 Smallest positive m such that m*n is free of prime gaps in canonical factorization. 4
1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 15, 1, 1, 1, 1, 1, 3, 5, 105, 1, 1, 1, 1155, 1, 15, 1, 1, 1, 1, 35, 15015, 1, 1, 1, 255255, 385, 3, 1, 5, 1, 105, 1, 4849845, 1, 1, 1, 3, 5005, 1155, 1, 1, 7, 15, 85085, 111546435, 1, 1, 1, 3234846615, 5, 1, 77, 35, 1, 15015, 1616615, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

A073490(n*a(n)) = 0, A137794(n*a(n)) = 1;

for m < a(n): A073490(n*m) > 0 and A137794(n*m) = 0;

a(A073491(n)) = 1; a(A073492(n) > 1.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..4096

Index entries for sequences computed from indices in prime factorization

EXAMPLE

n=42: A073490(42) = A073490([2*3]*[7]) = 1,

the gap is filled by a(42) = 5: A073490(42*5) = 0.

PROG

(PARI) A137795(n) = if(1==n, 1, my(f = factor(n), p = f[1, 1], gpf = f[#f~, 1], m = 1); while(p<gpf, if((n%p), m*=p); p = nextprime(1+p)); (m)); \\ Antti Karttunen, Sep 06 2018

CROSSREFS

Sequence in context: A262809 A331568 A010278 * A265025 A284578 A070989

Adjacent sequences:  A137792 A137793 A137794 * A137796 A137797 A137798

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Feb 11 2008

STATUS

approved

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Last modified May 27 11:47 EDT 2022. Contains 354097 sequences. (Running on oeis4.)