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Numbers n such that a^s + b^s + c^s + ... is prime, where a*b*c* ... is the prime factorization of n and s is the digital sum of n.
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%I #7 Dec 15 2017 17:36:50

%S 10,12,22,26,40,54,99,104,117,153,178,184,210,300,350,358,368,416,424,

%T 448,464,466,500,549,603,651,810,1020,1100,1116,1143,1190,1380,1528,

%U 1629,1726,1816,1860,1926,1952,2001,2097,2220,2400,2439,2523,2536,2613

%N Numbers n such that a^s + b^s + c^s + ... is prime, where a*b*c* ... is the prime factorization of n and s is the digital sum of n.

%C 959949 generates a prime with 227 digits: 3^45 + 3^45 + 106661^45.

%e 26 is in the sequence because 26 = 2*13 and 2^(2+6) + 13^(2+6) = 815730977, a prime.

%t abcsQ[n_]:=PrimeQ[Total[Flatten[Table[#[[1]],{#[[2]]}]&/@FactorInteger[ n]]^Total[IntegerDigits[n]]]]; Select[Range[3000],abcsQ] (* _Harvey P. Dale_, Feb 15 2016 *)

%Y Cf. A082813, A007953.

%K base,easy,nonn

%O 1,1

%A _Jason Earls_, Jun 20 2005