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 A239940 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A051674 is a subsequence of this sequence. LINKS Amiram Eldar, Table of n, a(n) for n = 1..147 EXAMPLE The arithmetic derivative of 508 is 512, phi(508) = 252, phi(512) = 256 and 508 - 252 = 512 - 256 = 256, so 508 is a term. MAPLE 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); MATHEMATICA 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 *) CROSSREFS Cf. A000010, A003415, A051674, A239726. Sequence in context: A316540 A066185 A330704 * A320923 A008107 A266958 Adjacent sequences: A239937 A239938 A239939 * A239941 A239942 A239943 KEYWORD nonn AUTHOR Paolo P. Lava, Mar 31 2014 EXTENSIONS More terms from Amiram Eldar, Mar 31 2019 STATUS approved

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Last modified April 20 02:14 EDT 2024. Contains 371798 sequences. (Running on oeis4.)