A082813 Prime numbers of form a^m + b^m + c^m + ..., where a*b*c* ... is the prime factorization of m.

539633, 43909277783870034878569768760415886733743786946105343887995366054267119200102384004474562849

Offset: 1

Author

N. J. A. Sloane, following a suggestion of G. L. Honaker, Jr., May 24 2003

Keywords

• nonn
• hard
• bref

Comments

No more terms with m < 822. - W. Edwin Clark, May 24 2003

No more terms with m < 10000. - Joint effort of Hugo Pfoertner and Joshua Zucker, May 30 2003

No more terms with m < 25500. - Martin Renner, Jan 31 2012

Examples

			a(1) = 539633 = 2^12 + 2^12 + 3^12 and 2*2*3 = 12.
a(2) is 2^88 + 2^88 + 2^88 + 11^88.
a(3) is 3^207 + 3^207 + 23^207.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..3
• G. L. Honaker, Jr., 539633
• Hugo Pfoertner, Program and input files for PFGW.

Crossrefs

Cf. A082814 for values of m.

Extensions

a(2) and a(3) from Joshua Zucker, May 24 2003. Their primality was confirmed by Hugo Pfoertner, May 24 2003.