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A068999
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Numbers k such that k = (sum of distinct prime factors of k)*(product of distinct prime factors of k).
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2
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4, 9, 25, 49, 121, 169, 289, 300, 361, 504, 529, 841, 961, 980, 1056, 1369, 1404, 1575, 1681, 1849, 2209, 2600, 2736, 2809, 3481, 3721, 4489, 4851, 5041, 5329, 6241, 6375, 6696, 6889, 7436, 7448, 7695, 7921, 9409, 9639, 10201, 10304, 10609, 11375, 11449
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OFFSET
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1,1
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COMMENTS
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Contains all squares of primes (A001248).
Terms that are not squares of primes: 300, 504, 980, 1056, 1404, 1575, 2600, 2736, 4851, 6375, 6696, 7436, 7448, 7695, 9639, 10304, 11375, 11583, 12384, 13376, 13770, 14144, 19250, 20691, 21500, 22656, 24548, 24975, 28175, 28944, 30008, 34983, 36848, 37026, 50024, 58400, 63455, ... - Alex Ratushnyak, Aug 17 2012
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LINKS
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EXAMPLE
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The prime factors of 300 are 2, 3, 5, the sum and product of which are 10, 30 respectively, which multiply to 300. Hence 300 belongs to the sequence.
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MATHEMATICA
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h[n_] := Module[{a, l }, a = FactorInteger[n]; l = Length[a]; Sum[a[[i]][[1]], {i, 1, l}]*Product[a[[i]][[1] ], {i, 1, l}] == n]; Select[Range[2, 10^4], h[ # ] &]
pf[n_] := First /@ FactorInteger[n]; Select[Range[11500], (Plus @@ pf[ # ])*(Times @@ pf[ # ]) == # &] (* Ray Chandler, Nov 14 2005 *)
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PROG
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(Python)
from sympy import primerange
import math
primes = list(primerange(2, 10000))
for n in range(1, 10000):
d = n
sum = 0
product = 1
for p in primes:
if d%p==0:
sum += p
product *= p
while d%p==0:
d//=p
if d==1:
break
if sum*product==n:
print(n, end=', ')
(Python)
from math import prod
from sympy import primefactors
def ok(n): pf = primefactors(n); return n == sum(pf)*prod(pf)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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