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 A068999 Numbers k such that k = (sum of distinct prime factors of k)*(product of distinct prime factors of k). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 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. MATHEMATICA 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 *) PROG (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=', ') # Alex Ratushnyak, Aug 18 2012 (Python) from math import prod from sympy import primefactors def ok(n): pf = primefactors(n); return n == sum(pf)*prod(pf) print(list(filter(ok, range(1, 11600)))) # Michael S. Branicky, May 15 2021 CROSSREFS Cf. A007947, A008472. Sequence in context: A158145 A082180 A246131 * A179707 A247078 A077438 Adjacent sequences: A068996 A068997 A068998 * A069000 A069001 A069002 KEYWORD nonn AUTHOR Joseph L. Pe, Mar 20 2002 EXTENSIONS Extended by Ray Chandler, Nov 14 2005 STATUS approved

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Last modified May 30 13:17 EDT 2023. Contains 363050 sequences. (Running on oeis4.)