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A175729
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Numbers n such that the sum of the prime factors with multiplicity of n divides n-1.
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2
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6, 21, 45, 52, 225, 301, 344, 441, 697, 1225, 1333, 1540, 1625, 1680, 1695, 1909, 2025, 2041, 2145, 2295, 2466, 2601, 2926, 3051, 3104, 3146, 3400, 3510, 3738, 3888, 3901, 4030, 4186, 4251, 4375, 4641, 4675, 4693, 4930, 5005, 5085, 5244, 5425, 6025, 6105
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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For example, 21=7x3, 7+3=10 which divides 21-1=20.
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MAPLE
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A001414 := proc(n) ifactors(n)[2] ; add( op(1, p)*op(2, p), p=%) ; end proc:
isA175729 := proc(n) if (n-1) mod A001414(n) = 0 then true; else false; end if; end proc:
for n from 2 to 10000 do if isA175729(n) then printf("%d, ", n) ; end if; end do:
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MATHEMATICA
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fQ[n_] := Mod[n - 1, Plus @@ Flatten[ Table[ #1, {#2}] & @@@ FactorInteger@ n]] == 0; Select[ Range@ 6174, fQ] (* Robert G. Wilson v, Aug 25 2010 *)
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PROG
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(Magma) [k:k in [2..6200]| IsIntegral((k-1)/( &+[m[1]*m[2]: m in Factorization(k)]))]; // Marius A. Burtea, Sep 16 2019
(Python)
from sympy import factorint
def ok(n): return n>1 and (n-1)%sum(p*e for p, e in factorint(n).items())==0
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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K. T. Lee (7x3(AT)21cn.com), Aug 23 2010
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EXTENSIONS
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STATUS
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approved
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