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A239940
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Numbers k such that phi(k) - k = phi(k') - k', where k' is the arithmetic derivative of k and phi(k) is the Euler totient function.
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2
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1, 4, 12, 27, 28, 124, 279, 508, 1175, 3125, 7767, 18125, 32764, 38205, 53757, 68013, 86999, 153575, 171549, 171875, 271875, 496341, 524284, 823543, 1160541, 1344573, 1900557, 1945233, 2097148, 2828375, 4175037, 4709853, 5625261, 6224013, 7768031, 10628469
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OFFSET
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1,2
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COMMENTS
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A051674 is a subsequence of this sequence.
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LINKS
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EXAMPLE
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The arithmetic derivative of 508 is 512, phi(508) = 252, phi(512) = 256 and 508 - 252 = 512 - 256 = 256, so 508 is a term.
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MAPLE
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with(numtheory); P:=proc(q) local a, n, p;
for n from 1 to q do a:=n*add(op(2, p)/op(1, p), p=ifactors(n)[2]);
if phi(a)-a=phi(n)-n then print(n); fi;
od; end: P(10^9);
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MATHEMATICA
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d[1] = 0; d[n_] := n*Total[#2/#1 & @@@ FactorInteger[n]]; p[n_] := EulerPhi[n] - n; seqQ[n_] := p[d[n]] == p[n]; Select[Range[100000], seqQ] (* Amiram Eldar, Mar 31 2019 *)
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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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