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

378, 2548, 2836295, 4473671462, 23040925705, 13579716377989, 21467102506955, 119429556097859

Offset: 1

Author

Naohiro Nomoto, Nov 21 2000

Keywords

• nonn
• more

Comments

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.

Repeated prime factors are used only once.

Examples

			378 = 2 * 3^3 * 7 = 2^3 + 3^3 + 7^3;
2548 = 2^2 * 7^2 * 13 = 2^3 + 7^3 + 13^3;
2836295 = 5 * 7 * 11 * 53 * 139 = 5^3 + 7^3 + 11^3 + 53^3 + 139^3;
4473671462 = 2 * 13 * 179 * 593 * 1621 = 2^3 + 13^3 + 179^3 + 593^3 + 1621^3;
23040925705 = 5 * 7 * 167 * 1453 * 2713 = 5^3 + 7^3 + 167^3 + 1453^3 + 2713^3;
13579716377989 = 19 * 157 * 173 * 1103 * 23857 = 19^3 + 157^3 + 173^3 + 1103^3 + 23857^3;
21467102506955 = 5 * 73 * 313 * 1439 * 27791 = 5^3 + 7^3 + 313^3 + 1439^3 + 27791^3;
119429556097859 = 7 * 53 * 937 * 6983 * 49199 = 7^3 + 53^3 + 937^3 + 6983^3 + 49199^3.
		

References

• J.-M. De Koninck and A. Mercier, 1001 Problèmes en Théorie Classique Des Nombres, Problem 261 pp. 186, Ellipses, Paris 2004.

Links

• Jean-Marie De Koninck, Partial Sums of Powers of Prime Factors, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.6
• J. M. de Koninck and Armel Mercier, 1001 Problems in Classical Number Theory, American Mathematical Society 2007. Page 160.

Crossrefs

Cf. A007412 (noncubes).

Programs

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

Extensions

Corrected definition and five more terms from Koffie Duah (admc1961(AT)live.com), Feb 16 2008