A078651 - OEIS

%I #7 Oct 24 2023 12:55:57

%S 1,3,5,9,11,15,17,23,27,31,33,40,42,46,50,59,61,68,70,77,81,85,87,97,

%T 101,105,111,118,120,128,130,141,145,149,153,165,167,171,175,185,187,

%U 195,197,204,211,215,217,231,235,242,246,253,255,265,269,279,283,287

%N Number of increasing geometric-progression subsequences of [1,...,n] with integral successive-term ratio and length >= 1.

%C The number of geometric-progression subsequences of [1,...,n] with integral successive-term ratio r and length k is floor(n/r^(k-1))(n > 0, r > 1, k > 0).

%F a(n) = n + sum {r > 1, j > 0} floor(n/r^j)

%e a(1): [1]; a(2): [1],[2],[1,2]; a(3): [1],[2],[3],[1,2],[1,3]

%Y a(n) = n + A078632(n).

%Y See A366471 for rational ratios.

%Y See A078567 for APs.

%K nonn,easy

%O 1,2

%A Robert E. Sawyer (rs.1(AT)mindspring.com), Jan 08, 2003