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A331526 a(n) is the least positive k such that A100273(n) - k^3 is a fifth power.

%I A331526 #14 Jan 20 2020 12:54:18
%S A331526 1,3,5,2,4,9,3,7,9,13,15,8,16,14,19,5,20,21,13,22,17,25,4,10,27,16,18,
%T A331526 29,24,33,31,35,4,39,8,39,36,20,22,41,42,28,44,46,7,13,19,47,48,38,46,
%U A331526 49,40,50,48,33,39,2,6,8,12,56,26,52,62,63,58,23,64,31
%N A331526 a(n) is the least positive k such that A100273(n) - k^3 is a fifth power.
%H A331526 Rémy Sigrist, <a href="/A331526/b331526.txt">Table of n, a(n) for n = 1..10000</a>
%H A331526 Rémy Sigrist, <a href="/A331526/a331526_1.gp.txt">PARI program for A331526</a>
%e A331526 The first terms, alongside A100273(n), are:
%e A331526   n   a(n)  A100273(n)
%e A331526   --  ----  -----------------
%e A331526    1     1     2 =  1^3 + 1^5
%e A331526    2     3    59 =  3^3 + 2^5
%e A331526    3     5   157 =  5^3 + 2^5
%e A331526    4     2   251 =  2^3 + 3^5
%e A331526    5     4   307 =  4^3 + 3^5
%e A331526    6     9   761 =  9^3 + 2^5
%e A331526    7     3  1051 =  3^3 + 4^5
%e A331526    8     7  1367 =  7^3 + 4^5
%e A331526    9     9  1753 =  9^3 + 4^5
%e A331526   10    13  3221 = 13^3 + 4^5
%o A331526 (PARI) See Links section.
%Y A331526 See A331435 for similar sequences.
%Y A331526 Cf. A000584, A100273.
%K A331526 nonn
%O A331526 1,2
%A A331526 _Rémy Sigrist_, Jan 19 2020