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.

A294284 Sum of the smaller parts of the partitions of n into two distinct parts with larger part squarefree.

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%I A294284 #24 Jun 22 2019 10:55:54
%S A294284 0,0,1,1,2,1,3,6,9,7,10,8,11,8,12,17,22,28,34,31,37,33,40,48,56,51,59,
%T A294284 53,60,53,61,70,79,72,82,93,104,97,109,122,135,128,142,135,149,140,
%U A294284 154,169,184,199,214,204,219,235,251,268,285,274,292,281
%N A294284 Sum of the smaller parts of the partitions of n into two distinct parts with larger part squarefree.
%C A294284 Sum of the widths of the distinct rectangles with squarefree length and positive integer width such that L + W = n, W < L. For example, a(13) = 11; the rectangles are 2 X 11, 3 X 10, 6 X 7. The sum of the widths is then 2 + 3 + 6 = 11. - _Wesley Ivan Hurt_, Nov 12 2017
%H A294284 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A294284 a(n) = Sum_{i=1..floor((n-1)/2)} i * mu(n-i)^2, where mu is the Möbius function (A008683).
%t A294284 Table[Sum[i*MoebiusMu[n - i]^2, {i, Floor[(n-1)/2]}], {n, 60}]
%o A294284 (PARI) a(n) = sum(i=1, (n-1)\2, i*moebius(n-i)^2); \\ _Michel Marcus_, Nov 05 2017
%Y A294284 Cf. A008683, A294145, A294285.
%K A294284 nonn,easy
%O A294284 1,5
%A A294284 _Wesley Ivan Hurt_, Oct 26 2017