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A230545
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Solutions of the equation n' = n + phi(n), where n' is the arithmetic derivative of n.
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1
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8, 12, 100, 140, 243, 405, 1372, 46875, 56644, 64827, 98260, 101871, 107811, 129375, 230692, 243675, 300820, 644204, 851175, 1953125, 3828125, 7948395, 19307236, 28218268, 36517316, 69330772, 70174377, 93961125, 115008417, 173353125, 181010116, 267603885, 404021709
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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For n = 1372 we have phi(n) = 588, n' = 1960 and 1960 = 1372 + 588.
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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]);
if a1=n+phi(n) then print(n); fi; od; end: P(10^6);
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PROG
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(PARI) for(n=2, 10^10, if((k = n + eulerphi(n)) && (d(n) = local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))) && k==d(n), print1(n", "))) \\ Altug Alkan, Oct 06 2015
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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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STATUS
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approved
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