A070006 Composite numbers that are not a prime power and whose distinct prime divisors' arithmetic mean is a prime.

21, 33, 57, 63, 69, 85, 93, 99, 105, 129, 133, 145, 147, 171, 177, 189, 195, 205, 207, 213, 217, 231, 237, 249, 253, 265, 279, 297, 309, 315, 363, 387, 393, 417, 425, 441, 445, 465, 469, 483, 489, 493, 505, 513, 517, 525, 531, 553, 565, 567, 573, 585, 597

Offset

1,1

Comments

Subsequence of A070005.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

n = 993 = 3*331, mean = 334/2 = 167, a prime.

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] Do[s=Apply[Plus, ba[n]]/lf[n]; If[PrimeQ[s]&&Greater[lf[n], 1], Print[n]], {n, 2, 1000}]
(* Second program: *)
Select[Range@ 600, And[! PrimePowerQ@ #, PrimeQ@ Mean[FactorInteger[#][[All, 1]]]] &] (* Michael De Vlieger, Jul 18 2017 *)

Prog

(PARI) lista(nn) = {for (n=2, nn, f = factor(n); if ((#f~ != 1) && (type(q=sum(k=1, #f~, f[k, 1])/#f~) == "t_INT") && isprime(q), print1(n, ", ")); ); } \\ Michel Marcus, Mar 28 2015

Crossrefs

Cf. A001414, A008472, A070005.

Sequence in context: A330441 A176945 A333857 * A189986 A190299 A280262

Adjacent sequences: A070003 A070004 A070005 * A070007 A070008 A070009

Keyword

easy,nonn

Author

Labos Elemer, Apr 11 2002

Status

approved