A108703 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.

10, 12, 22, 26, 40, 54, 99, 104, 117, 153, 178, 184, 210, 300, 350, 358, 368, 416, 424, 448, 464, 466, 500, 549, 603, 651, 810, 1020, 1100, 1116, 1143, 1190, 1380, 1528, 1629, 1726, 1816, 1860, 1926, 1952, 2001, 2097, 2220, 2400, 2439, 2523, 2536, 2613

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..48.

Example

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

Mathematica

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

Crossrefs

Cf. A082813, A007953.

Sequence in context: A061870 A348056 A120001 * A098785 A022324 A084953

Adjacent sequences: A108700 A108701 A108702 * A108704 A108705 A108706

Keyword

base,easy,nonn

Author

Jason Earls, Jun 20 2005

Status

approved