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

1,8

Links

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

Formula

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

Example

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).

Prog

(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

Crossrefs

Cf. A058189.

Sequence in context: A230819 A317573 A032337 * A055736 A006997 A141612

Adjacent sequences: A058187 A058188 A058189 * A058191 A058192 A058193

Keyword

nonn

Author

Henry Bottomley, Nov 22 2000

Status

approved