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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
LINKS
FORMULA
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.
a(n) = A083720(n) / A034386(A020639(n)-1). - Peter Munn, Feb 24 2024
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 11 2008
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)