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
Examples
n = 993 = 3*331, mean = 334/2 = 167, a prime.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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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 *) -
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
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