A134620 Numbers such that the sum of 4th power of their prime factors is a prime.

6, 10, 12, 14, 22, 34, 38, 40, 45, 46, 74, 82, 117, 118, 122, 126, 142, 152, 158, 171, 194, 231, 262, 278, 296, 345, 358, 363, 376, 384, 387, 429, 432, 446, 454, 458, 482, 486, 490, 500, 507, 522, 536, 550, 566, 584, 626, 627, 634, 639, 663, 675, 686, 704, 705

Offset: 1

Author

Hieronymus Fischer, Nov 11 2007

Keywords

• nonn

Comments

Prime factors must be taken with multiplicity. - Harvey P. Dale, May 23 2012

The calculation of higher terms is time-consuming, since for any number of the form 2*p with a prime number p > 10^5 the primality test have to be accomplished for a number > 10^20. - Hieronymus Fischer, May 21 2013

Examples

			a(2) = 10, since 10 = 2*5 and 2^4+5^4 = 641 which is prime.
a(9) = 45, since 45 = 3*3*5 and 3^4+3^4+5^4 = 787 which is prime.
a(9883) = 333314, since 333314 = 3*166657 and 2^4+166657^4 = 771425941499397811217 which is prime.
		

Links

• Harvey P. Dale and Hieronymus Fischer, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A001597, A025475, A134333, A134344, A134376.

Cf. A134600, A134602, A134605, A134608, A134612, A134616, A134618, A134621.

Programs

Mathematica

Select[Range[1000],PrimeQ[Total[Flatten[Table[First[#],{Last[#]}]&/@ FactorInteger[#]]^4]]&] (* Harvey P. Dale, May 23 2012 *)