A058190 Number of increasing geometric progressions ending in n (in the positive integers), excluding those of length 1 or 2.

0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 5, 0, 2, 0, 1, 0, 0, 0, 2, 4, 0, 4, 1, 0, 0, 0, 6, 0, 0, 0, 5, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 0, 5, 6, 4, 0, 1, 0, 4, 0, 2, 0, 0, 0, 1, 0, 0, 2, 13, 0, 0, 0, 1, 0, 0, 0, 6, 0, 0, 4, 1, 0, 0, 0, 5, 12, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 6, 0, 6, 2, 9, 0, 0, 0

Offset: 1

Author

Henry Bottomley, Nov 22 2000

Keywords

• nonn

Examples

			a(16) = 5 since the possibilities are (1,4,16), (1,2,4,8,16), (2,4,8,16), (4,8,16), (9,12,16).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A058189.

Programs

PARI

ends_max_progression_of_length(n,ratio) = { my(k=1); while(1,if(denominator(n)>1,return(k)); n *= ratio; k++;) };
A058190(n) = sum(d=1,(n-1),max(0,ends_max_progression_of_length(d,d/n)-2)); \\ Antti Karttunen, Nov 19 2017

Formula

a(n) = A058189(n) - n.