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%I #25 May 15 2021 12:34:46
%S 4,9,25,49,121,169,289,300,361,504,529,841,961,980,1056,1369,1404,
%T 1575,1681,1849,2209,2600,2736,2809,3481,3721,4489,4851,5041,5329,
%U 6241,6375,6696,6889,7436,7448,7695,7921,9409,9639,10201,10304,10609,11375,11449
%N Numbers k such that k = (sum of distinct prime factors of k)*(product of distinct prime factors of k).
%C Contains all squares of primes (A001248).
%C 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
%H Amiram Eldar, <a href="/A068999/b068999.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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[ # ] &]
%t pf[n_] := First /@ FactorInteger[n]; Select[Range[11500], (Plus @@ pf[ # ])*(Times @@ pf[ # ]) == # &] (* _Ray Chandler_, Nov 14 2005 *)
%o (Python)
%o from sympy import primerange
%o import math
%o primes = list(primerange(2,10000))
%o for n in range(1,10000):
%o d = n
%o sum = 0
%o product = 1
%o for p in primes:
%o if d%p==0:
%o sum += p
%o product *= p
%o while d%p==0:
%o d//=p
%o if d==1:
%o break
%o if sum*product==n:
%o print(n, end=',')
%o # _Alex Ratushnyak_, Aug 18 2012
%o (Python)
%o from math import prod
%o from sympy import primefactors
%o def ok(n): pf = primefactors(n); return n == sum(pf)*prod(pf)
%o print(list(filter(ok, range(1, 11600)))) # _Michael S. Branicky_, May 15 2021
%Y Cf. A007947, A008472.
%K nonn
%O 1,1
%A _Joseph L. Pe_, Mar 20 2002
%E Extended by _Ray Chandler_, Nov 14 2005
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