|
|
A071837
|
|
Numbers k with the property that in the prime factorization of k all prime exponents are prime, their sum is also prime and equals the sum of distinct prime factors of k.
|
|
2
|
|
|
4, 27, 72, 108, 800, 3125, 12500, 247808, 823543, 37879808, 190512000, 266716800, 428652000, 529200000, 600112800, 1234800000, 1452124800, 2420208000, 2679075000, 3307500000, 7351381800, 7441875000, 7717500000, 9376762500
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
EXAMPLE
|
800 is a term as 800 = 2^5 * 5^2, 2+5 = 5+2 = 7, and 7,5,2 are primes.
|
|
MATHEMATICA
|
terms = 24; fromFactors[s_List] := (Times @@ (s^#)&) /@ Permutations[s]; Clear[f]; f[n_] := f[n] = (ssp = Select[Subsets[Prime[Range[n]]] // Rest, PrimeQ[Total[#]]&]; fromFactors /@ ssp // Flatten // Union // PadRight[#, terms]& ); f[2]; f[n = 4]; While[Print["n = ", n]; f[n] != f[n-2], n = n+2]; f[n] (* Jean-François Alcover, Jul 20 2015 *)
|
|
PROG
|
(PARI) isok(n) = {f = factor(n); for (i=1, #f~, if (! isprime(f[i, 2]), return (0)); ); isprime(se = sum(i=1, #f~, f[i, 2])) && (se == sum(i=1, #f~, f[i, 1])); } \\ Michel Marcus, Aug 21 2014
(Python)
from sympy import factorint, isprime
for n in range(1, 10**5):
....f = factorint(n)
....fp, fe = list(f.keys()), list(f.values())
....if sum(fp) == sum(fe) and isprime(sum(fe)) and all([isprime(e) for e in fe]):
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|