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A046346
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Composite numbers that are divisible by the sum of their prime factors (counted with multiplicity).
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23
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4, 16, 27, 30, 60, 70, 72, 84, 105, 150, 180, 220, 231, 240, 256, 286, 288, 308, 378, 440, 450, 476, 528, 540, 560, 576, 588, 594, 624, 627, 646, 648, 650, 728, 800, 805, 840, 884, 897, 900, 945, 960, 1008, 1040, 1056, 1080, 1100, 1122, 1134, 1160, 1170, 1248
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OFFSET
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1,1
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COMMENTS
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If m is in the sequence and d|m, then m^d is also a term. Note that this sequence contains all infinite subsequences of the form p^(p^k) for k>0, where p is a prime. - Amiram Eldar and Thomas Ordowski, Feb 06 2019
If one selects some composite k, k >= 8, and decomposes (k - sopfr(k)) into an additive partition having only prime parts, then those parts, when taken as a product with k, yield an element of this sequence. - Christopher Hohl, Jul 30 2019
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LINKS
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EXAMPLE
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a(38) = 884 = 2 * 2 * 13 * 17 -> 2 + 2 + 13 + 17 = 34 so 884 / 34 = 26.
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MAPLE
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isA046346 := proc(n)
if isprime(n) then
false;
true;
else
false;
end if;
end proc:
for n from 2 to 1000 do
if isA046346(n) then
printf("%d, ", n);
end if;
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MATHEMATICA
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Select[Range[2, 1170], !PrimeQ[#]&&IntegerQ[#/Total[Times@@@FactorInteger[#]]]&] (* Jayanta Basu, Jun 02 2013 *)
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PROG
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(PARI) sopfr(n) = {my(f=factor(n)); sum(k=1, #f~, f[k, 1]*f[k, 2]); }
lista(nn) = forcomposite(n=2, nn, if (! (n % sopfr(n)), print1(n, ", ")); ); \\ Michel Marcus, Jan 06 2016
(MATLAB) m=1; for u=2:1200 if and(isprime(u)==0, mod(u, sum(factor(u)))==0); sol(m)=u; m=m+1; end; end; sol % Marius A. Burtea, Jul 31 2019
(Magma) [k:k in [2..1200]| not IsPrime(k) and k mod (&+[m[1]*m[2]: m in Factorization(k)]) eq 0]; // Marius A. Burtea, Jul 31 2019
(Python)
from sympy import factorint
def ok(n):
f = factorint(n)
return sum(f[p] for p in f) > 1 and n % sum(p*f[p] for p in f) == 0
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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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Description corrected by Robert A. Stump (bee_ess107(AT)yahoo.com), Jan 09 2002
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STATUS
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approved
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