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

539633, 43909277783870034878569768760415886733743786946105343887995366054267119200102384004474562849

Offset

1,1

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

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.

Example

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.

Crossrefs

Cf. A082814 for values of m.

Sequence in context: A237323 A251355 A043636 * A204345 A269323 A043667

Adjacent sequences: A082810 A082811 A082812 * A082814 A082815 A082816

Keyword

nonn,hard,bref

Author

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

Extensions

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

Status

approved