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A071837 Numbers n with property that in the prime factorization of n all prime exponents are prime, their sum is also prime and equals the sum of distinct prime factors of n. 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

Table of n, a(n) for n=1..24.

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-Fran├žois 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

A071837 = []

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]):

........A071837.append(n)

# Chai Wah Wu, Aug 27 2014

CROSSREFS

Cf. A054411, A008472, A001222, A056166, A070215.

A240983 and A051674 are subsequences. - Zak Seidov, Aug 21 2014

Sequence in context: A122405 A122406 A276372 * A266011 A015238 A298987

Adjacent sequences:  A071834 A071835 A071836 * A071838 A071839 A071840

KEYWORD

nonn,nice

AUTHOR

Reinhard Zumkeller, Jun 08 2002

STATUS

approved

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Last modified August 25 13:50 EDT 2019. Contains 326324 sequences. (Running on oeis4.)