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
Keywords
Examples
a(4) = 5 since the possibilities are (4), (1,4), (2,4), (3,4) and (1,2,4).
Links
- Antti Karttunen, Table of n, a(n) for n = 1..16384
Programs
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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
Formula
a(n) = A058190(n) + n.