A243284 a(n) = the number of distinct ways of writing such products m = k^2 * j, 0 < j <= k, (j and k natural numbers) that m is in range [1,n]; Partial sums of A102354.

1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 17

Offset

1,4

Comments

a(n) = the number of distinct ways of writing such products m = k^2 * j, 0 < j <= k, (j and k natural numbers) that m is in range [1,n].

Different ways to write product for the same m are counted separately, e.g. for 64, both 8^2 * 1 and 4^2 * 4 are counted, so a(64) = a(63)+2 = 13+2 = 15.

Differs from A243283 for the first time at n=48, where a(48)=11, while A243283(48)=10. This is because 48 = 2*2*2*2*3 is the first integer which can be represented in the form k^2 * j, 0 < j <= k (namely as 48 = 4^2 * 3), even though it is not a member of A070003.

Links

Table of n, a(n) for n=1..75.

Crossrefs

Partial sums of A102354.

Cf. A243283, A013928, A057627.

Sequence in context: A217038 A309196 A243283 * A338623 A072613 A029551

Adjacent sequences: A243281 A243282 A243283 * A243285 A243286 A243287

Keyword

nonn

Author

Antti Karttunen, Jun 02 2014

Status

approved