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

Author

Reinhard Zumkeller, Feb 11 2008

Keywords

• nonn

Examples

			n=42: A073490(42) = A073490([2*3]*[7]) = 1,
the gap is filled by a(42) = 5: A073490(42*5) = 0.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4096
• Index entries for sequences computed from indices in prime factorization

Crossrefs

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

Programs

PARI

A137795(n) = if(1==n,1, my(f = factor(n), p = f[1, 1], gpf = f[#f~, 1], m = 1); while(pAntti Karttunen, Sep 06 2018

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