cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A243284 #8 Jun 05 2014 01:31:07
%S A243284 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,
%T A243284 9,10,10,10,10,10,10,10,10,10,10,10,10,11,12,13,13,13,13,13,13,13,13,
%U A243284 13,13,13,13,13,13,15,15,15,15,15,15,15,15,16,16,16,17
%N 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.
%C 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].
%C A243284 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.
%C A243284 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.
%Y A243284 Partial sums of A102354.
%Y A243284 Cf. A243283, A013928, A057627.
%K A243284 nonn
%O A243284 1,4
%A A243284 _Antti Karttunen_, Jun 02 2014