A088043 - OEIS

%I #8 Sep 24 2023 04:31:35

%S 1,2,3,4,3,6,4,6,5,6,3,10,4,7,8,8,3,10,3,10,9,6,3,14,5,7,7,11,3,15,5,

%T 10,7,6,8,16,3,6,8,15,3,16,4,10,12,6,3,18,6,10,7,11,3,14,7,15,8,6,3,

%U 23,3,8,14,12,8,14,3,10,7,15,3,22,4,6,12,10,8,15,3,19,9,6,3,24,8,7,7,14,3,23

%N Number of partitions of n into parts which can be arranged to form a geometric progression (possibly with a common ratio of 1). (For every partition there exists a geometric progression in which this partition fits in as successive terms.).

%e a(15) = 8 and the partitions are (15), (5, 5, 5), (3, 3, 3, 3, 3), (1, 1, ...15 times), (1, 2, 4, 8), (5, 10), (1, 14), (3, 12).

%e a(31) = 5 and the partitions are (31), (1+1...,31 times), (1,5,25),(1,2,4,8,16), (1,30).

%o (PARI) lim = 100; A = vector(lim, i, 1); for (r = 1, lim - 1, s = r + 1; while (s <= lim, forstep (k = s, lim, s, A[k]++); s = r*s + 1)); A \\ _David Wasserman_, Jun 21 2005

%Y Cf. A049988.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Sep 20 2003

%E More terms from _David Wasserman_, Jun 21 2005