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A331525 a(n) is the least positive k such that A100272(n) - k^2 is a fifth power.

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%I A331525 #14 Jan 20 2020 12:54:05
%S A331525 1,2,4,6,3,10,9,14,15,8,20,14,16,24,20,26,22,27,26,3,5,13,15,36,34,23,
%T A331525 40,27,33,44,37,51,54,45,56,18,58,24,53,63,55,57,64,66,36,69,42,63,74,
%U A331525 75,73,82,84,66,86,90,93,92,31,94,35,78,99,49,84,100,97
%N A331525 a(n) is the least positive k such that A100272(n) - k^2 is a fifth power.
%H A331525 Rémy Sigrist, <a href="/A331525/b331525.txt">Table of n, a(n) for n = 1..10000</a>
%H A331525 Rémy Sigrist, <a href="/A331525/a331525_1.gp.txt">PARI program for A331525</a>
%e A331525 The first terms, alongside A100272(n), are:
%e A331525   n   a(n)  A100272(n)
%e A331525   --  ----  ----------------
%e A331525    1     1    2 =  1^2 + 1^5
%e A331525    2     2    5 =  2^2 + 1^5
%e A331525    3     4   17 =  4^2 + 1^5
%e A331525    4     6   37 =  6^2 + 1^5
%e A331525    5     3   41 =  3^2 + 2^5
%e A331525    6    10  101 = 10^2 + 1^5
%e A331525    7     9  113 =  9^2 + 2^5
%e A331525    8    14  197 = 14^2 + 1^5
%e A331525    9    15  257 = 15^2 + 2^5
%e A331525   10     8  307 =  8^2 + 3^5
%o A331525 (PARI) See Links section.
%Y A331525 See A331435 for similar sequences.
%Y A331525 Cf. A000584, A100272.
%K A331525 nonn
%O A331525 1,2
%A A331525 _Rémy Sigrist_, Jan 19 2020