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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)

#primes = [ 2, 3, ... ]

import math

for n in range(1, 100000):

    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:

        #s = int(math.sqrt(n))

        #if s*s != n or (s not in primes):

            print n,

# Alex Ratushnyak, Aug 18 2012

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 November 20 20:46 EST 2019. Contains 329347 sequences. (Running on oeis4.)