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A230544
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Solutions of the equation n'' = tau(n) * n', where n' and n'' are the first and the second arithmetic derivative of n.
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0
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1, 1255, 4063, 5359, 6583, 8615, 11623, 12047, 14359, 14863, 15943, 27644, 32471, 49271, 52607, 81599, 98471, 101687, 117647, 164327, 173447, 176471, 203327, 209207, 235271, 246647, 277271, 301607, 343271, 355871, 358367, 360623, 378047, 392471, 401927, 406607
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OFFSET
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1,2
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LINKS
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EXAMPLE
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For n = 6583 we have tau(n) = 4, n’ = 256, n’’= 1024 and 1024 = 4 * 256.
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MAPLE
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with(numtheory); P:= proc(q) local a1, a2, n, p;
for n from 1 to q do a1:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]); ;
a2:=a1*add(op(2, p)/op(1, p), p=ifactors(a1)[2]);
if a2=tau(n)*a1 then print(n); fi; od; end: P(10^6);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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