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.
%I A351064 #26 Apr 30 2022 01:14:56 %S A351064 1,2,3,1,2,3,4,1,1,2,3,2,3,4,5,1,2,3,4,2,3,4,5,2,1,2,1,2,3,4,2,1,2,3, %T A351064 4,1,2,3,4,2,2,3,2,2,3,4,3,2,1,2,3,2,3,4,5,3,2,3,2,3,4,5,2,1,2,3,4,2, %U A351064 3,4,5,2,2,3,3,2,3,4,3,2,1,2,3,3,2,3,4,3,2,2,2,3,3,4,3,2,2,3,4,1,2,3,4,3,3,2 %N A351064 Minimal number of positive perfect powers, with different exponents, whose sum is n (considering only minimal possible exponents for bases equal to 1). %C A351064 Conjecture: the only numbers for which 5 addends are needed are 15, 23, 55, 62, 71. %C A351064 The numbers mentioned in the conjecture are also the first five terms of A111151. - _Omar E. Pol_, Mar 01 2022 %e A351064 a(1) = 1 because 1 can be represented with a single positive perfect power: 1 = 1^2. %e A351064 a(2) = 2 because 2 can be represented with two (and not fewer) positive perfect powers with different exponents: 2 = 1^2 + 1^3. %e A351064 a(6) = 3 because 6 can be represented with three (and not fewer) positive perfect powers with different exponents: 6 = 2^2 + 1^3 + 1^4. %e A351064 a(7) = 4 because 7 can be represented with four (and not fewer) positive perfect powers with different exponents: 7 = 2^2 + 1^3 + 1^4 + 1^5. %e A351064 a(15) = 5 because 15 can be represented with five (and not fewer) positive perfect powers with different exponents: 15 = 2^2 + 2^3 + 1^4 + 1^5 + 1^6. %Y A351064 Cf. A111151, A351062, A351063, A351066. %K A351064 nonn %O A351064 1,2 %A A351064 _Alberto Zanoni_, Feb 22 2022