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A199745
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Numbers such that the sum of the largest and the smallest prime divisor equals the sum of the other distinct prime divisors.
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4
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2145, 2730, 4641, 4845, 5005, 5460, 5610, 6435, 7410, 8190, 8778, 9177, 10725, 10920, 11220, 11305, 11730, 13485, 13585, 13650, 13923, 14535, 14820, 16380, 16830, 17017, 17556, 19110, 19305, 20010, 20930, 21489, 21505, 21840, 22230, 22440, 23460, 23529, 23595
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The definition implies that members of the sequence have at least four distinct prime factors. An even term must have at least five distinct prime factors.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
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FORMULA
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n such that A008472(n)/2 = A074320(n) = A020639(n) + A006530 (n). - Ray Chandler, Nov 10 2011
Sum_{k=2..A001221(a(n))} A027748(a(n),k) = A027748(a(n),1) + A027748(a(n), A001221(a(n))). - Reinhard Zumkeller, Nov 10 2011
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EXAMPLE
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22440 is in the sequence because the distinct prime divisors are {2, 3, 5, 11, 17} and 17+2 = 3+5+11.
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MAPLE
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isA199745 := proc(n)
local p;
p := sort(convert(numtheory[factorset](n), list)) ;
if nops(p) >= 3 then
return ( op(1, p) + op(-1, p) = add(op(i, p), i=2..nops(p)-1) ) ;
else
false;
end if;
end proc:
for n from 2 to 20000 do
if isA199745(n) then
printf("%d, ", n) ;
end if ;
end do: # R. J. Mathar, Nov 10 2011
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MATHEMATICA
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Select[Range[25000], Plus@@(pl=First/@FactorInteger[#])/2==pl[[1]]+pl[[-1]]&] (* Ray Chandler, Nov 10 2011 *)
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PROG
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(Sage)
def isA199745(n) :
p = factor(n)
return len(p) > 2 and p[0][0] + p[-1][0] == add(p[i][0] for i in (1..len(p)-2))
[n for n in (2..20000) if isA199745(n)] # Peter Luschny, Nov 10 2011
(Haskell)
a199745 n = a199745_list !! (n-1)
a199745_list = filter (\x -> 2 * (a074320 x) == a008472 x) [1..]
-- Reinhard Zumkeller, Nov 10 2011
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CROSSREFS
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Cf. A020639, A006530, A074320, A008472, A109353.
Sequence in context: A347040 A252547 A211601 * A200145 A179271 A118576
Adjacent sequences: A199742 A199743 A199744 * A199746 A199747 A199748
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KEYWORD
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nonn
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AUTHOR
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Michel Lagneau, Nov 09 2011
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STATUS
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approved
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