cp's OEIS Frontend

A383122 a(n) is the smallest number that can be expressed as the sum of the smallest number of powers with different exponents greater than one in n different ways (for unitary bases, the smallest possible exponents are considered).

%I A383122 #11 Apr 18 2025 22:24:52
%S A383122 1,16,17,65,80,105,139,193,329,313,336,410,477,273,553,461,436,1219,
%T A383122 942,10153,1595,1038,722,636,1769,1344,2045,2381,1805,2379,3683,2365,
%U A383122 1611,3319,3815,4416,4838,4029,3531,5606,5789,4411,4341,5849,7392,1642,4885,8246,3074,5251,5774,3165,2498,12347,9987,5405,8075,11101,2346,6749
%N A383122 a(n) is the smallest number that can be expressed as the sum of the smallest number of powers with different exponents greater than one in n different ways (for unitary bases, the smallest possible exponents are considered).
%C A383122 The sequence is infinite.
%H A383122 Eugenio Garista and Alberto Zanoni, <a href="http://www.mathesis.verona.it/wp-content/uploads/2018/Numeri/Nume317.pdf">Somme di potenze con esponenti diversi</a>, MatematicaMente, 317 (2024), 1-2.
%H A383122 Eugenio Garista and Alberto Zanoni, <a href="https://armjmath.sci.am/index.php/ajm/article/view/1347/261">Sums of Positive Integer Powers with Unlike Exponents</a>, Armenian Journal of Mathematics, 17 No. 3 (2025), 1-11.
%H A383122 Alberto Zanoni, <a href="https://sum-of-unlike-powers.jimdosite.com/">Sum of unlike powers for integers</a>
%e A383122 For n = 1 the sum (1 addend) is 1^2
%e A383122 For n = 2 the sums (1 addend) are 4^2, 2^4
%e A383122 For n = 3 the sums are (2 addends) 1^2 + 2^4, 3^2 + 2^3, 4^2 + 1^3
%e A383122 For n = 4 the sums are (2 addends) 1^2 + 2^6, 1^2 + 4^3, 7^2 + 2^4, 8^2 + 1^3
%e A383122 For n = 5 the sums are (2 addends) 2^4 + 2^6, 4^3 + 2^4, 4^2 + 2^6, 4^2 + 4^3, 8^2 + 2^4
%e A383122 For n = 6 the sums are (3 addends) 3^2 + 2^5 + 2^6, 3^2 + 4^3 + 2^5, 4^2 + 2^3 + 3^4, 5^2 + 2^4 + 2^6, 5^2 + 4^3 + 2^4, 9^2 + 2^3 + 2^4
%Y A383122 Cf. A351062, A351066, A351063, A351065, A351064.
%K A383122 nonn
%O A383122 1,2
%A A383122 _Alberto Zanoni_, Apr 17 2025