A137795 Smallest positive m such that m*n is free of prime gaps in canonical factorization.

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

Offset

1,10

Links

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

Index entries for sequences computed from indices in prime factorization

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

Cf. A020639, A034386, A073490, A073491, A073492, A083720, A137794.

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