cp's OEIS Frontend

A058041 Noncubes equal to the sum of cubes of their prime factors.

%I A058041 #13 Dec 25 2018 11:29:47
%S A058041 378,2548,2836295,4473671462,23040925705,13579716377989,
%T A058041 21467102506955,119429556097859
%N A058041 Noncubes equal to the sum of cubes of their prime factors.
%C A058041 Let (p_1,p_2,...,p_m) = prime factors of n (m>1, k>0); sequence gives n such that n = Sum_{i=1,2,..,m} (p_i)^3.
%C A058041 Repeated prime factors are used only once.
%D A058041 J.-M. De Koninck and A. Mercier, 1001 Problèmes en Théorie Classique Des Nombres, Problem 261 pp. 186, Ellipses, Paris 2004.
%H A058041 Jean-Marie De Koninck, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL10/Koninck/koninck71.html">Partial Sums of Powers of Prime Factors</a>, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.6
%H A058041 J. M. de Koninck and Armel Mercier, <a href="http://www.ams.org/bookpages/pint/">1001 Problems in Classical Number Theory</a>, American Mathematical Society 2007. Page 160.
%e A058041 378 = 2 * 3^3 * 7 = 2^3 + 3^3 + 7^3;
%e A058041 2548 = 2^2 * 7^2 * 13 = 2^3 + 7^3 + 13^3;
%e A058041 2836295 = 5 * 7 * 11 * 53 * 139 = 5^3 + 7^3 + 11^3 + 53^3 + 139^3;
%e A058041 4473671462 = 2 * 13 * 179 * 593 * 1621 = 2^3 + 13^3 + 179^3 + 593^3 + 1621^3;
%e A058041 23040925705 = 5 * 7 * 167 * 1453 * 2713 = 5^3 + 7^3 + 167^3 + 1453^3 + 2713^3;
%e A058041 13579716377989 = 19 * 157 * 173 * 1103 * 23857 = 19^3 + 157^3 + 173^3 + 1103^3 + 23857^3;
%e A058041 21467102506955 = 5 * 73 * 313 * 1439 * 27791 = 5^3 + 7^3 + 313^3 + 1439^3 + 27791^3;
%e A058041 119429556097859 = 7 * 53 * 937 * 6983 * 49199 = 7^3 + 53^3 + 937^3 + 6983^3 + 49199^3.
%o A058041 (PARI) isok(n) = if (!ispower(n, 3), my(f=factor(n)); sum(k=1, #f~, f[k,1]^3) == n); \\ _Michel Marcus_, Dec 25 2018
%Y A058041 Cf. A007412 (noncubes).
%K A058041 nonn,more
%O A058041 1,1
%A A058041 _Naohiro Nomoto_, Nov 21 2000
%E A058041 Corrected definition and five more terms from Koffie Duah (admc1961(AT)live.com), Feb 16 2008