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A134619
Numbers such that the arithmetic mean of the cubes of their prime factors (taken with multiplicity) is a prime.
14
20, 44, 188, 297, 336, 400, 425, 540, 575, 605, 704, 752, 764, 908, 912, 1025, 1053, 1124, 1172, 1183, 1365, 1380, 1412, 1420, 1452, 1475, 1484, 1519, 1604, 1625, 1809, 1844, 1856, 1936, 1953, 2107, 2192, 2205, 2255, 2320, 2325, 2348, 2368, 2372, 2468
OFFSET
1,1
LINKS
EXAMPLE
a(10)=605, since 605=5*11*11 and (5^3+11^3+11^3)/3=929 which is prime.
MATHEMATICA
amcpfQ[n_]:=PrimeQ[Mean[Flatten[PadRight[{}, #[[2]], #[[1]]]&/@FactorInteger[n]]^3]]; Select[ Range[ 2500], amcpfQ] (* Harvey P. Dale, Jun 06 2023 *)
PROG
(PARI) lista(m) = {for (i=2, m, f = factor(i); s = sum (j=1, length(f~), f[j, 1]^3*f[j, 2]); s /= bigomega(i); if (type(s) == "t_INT" && isprime(s), print1(i, ", ")); ); } \\ Michel Marcus, Apr 14 2013
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Nov 11 2007
EXTENSIONS
Minor edits by Hieronymus Fischer, May 06 2013
STATUS
approved