A058189 Number of increasing geometric progressions ending in n (in the positive integers), including those of length 1 or 2.

1, 2, 3, 5, 5, 6, 7, 10, 11, 10, 11, 13, 13, 14, 15, 21, 17, 20, 19, 21, 21, 22, 23, 26, 29, 26, 31, 29, 29, 30, 31, 38, 33, 34, 35, 41, 37, 38, 39, 42, 41, 42, 43, 45, 47, 46, 47, 53, 55, 54, 51, 53, 53, 58, 55, 58, 57, 58, 59, 61, 61, 62, 65, 77, 65, 66, 67, 69, 69, 70, 71

Offset

1,2

Links

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

Formula

a(n) = A058190(n) + n.

Example

a(4) = 5 since the possibilities are (4), (1,4), (2,4), (3,4) and (1,2,4).

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));
A058189(n) = (A058190(n)+n); \\ Antti Karttunen, Nov 19 2017

Crossrefs

Cf. A054519 for arithmetic progressions.

Cf. A058190.

Sequence in context: A067535 A076752 A079114 * A361676 A069208 A346616

Adjacent sequences: A058186 A058187 A058188 * A058190 A058191 A058192

Keyword

nonn

Author

Henry Bottomley, Nov 22 2000

Status

approved