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 A243996 Numbers n such that phi(sigma*(n)) = sigma*(phi(n)), where sigma*(n) is the sum of anti-divisors of n and phi(n) is the Euler totient function. 1
 7, 9, 20, 25, 80, 143, 825, 3117, 3216, 22774, 52026, 55804, 138276, 187733, 228384, 265545, 320766, 549540, 830814, 839784, 901376, 1293552, 1315776, 2635866, 6771114, 11126800, 12087848, 24351460, 49382242, 52344292, 60063744, 65980038, 78279016, 97638080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(70) > 10^10. - Hiroaki Yamanouchi, Sep 28 2015 LINKS Hiroaki Yamanouchi, Table of n, a(n) for n = 1..69 EXAMPLE sigma*(phi(25)) = sigma*(20) = 24, phi(sigma*(25)) = phi(39) = 24. MAPLE with(numtheory): P:=proc(q) local a, b, c, d, j, k, n; for n from 1 to q do k:=0; j:=n; while j mod 2<>1 do k:=k+1; j:=j/2; od; a:=sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^k)*2^(k+1)-6*n-2; k:=0; c:=phi(n); j:=phi(n); while j mod 2<>1 do k:=k+1; j:=j/2; od; b:=sigma(2*c+1)+sigma(2*c-1)+sigma(c/2^k)*2^(k+1)-6*c-2; if b=phi(a) then print(n); fi; od; end: P(10^10); MATHEMATICA antiDivisors[n_] := Select[ Union[ Join[ Select[ Divisors[2 n - 1], OddQ[#] && # != 1 &], Select[ Divisors[ 2n + 1], OddQ[#] && # != 1 &], 2n/Select[ Divisors[ 2n], OddQ[#] && # != 1 &]]], # < n &]; fQ[n_] := EulerPhi@ Total@ antiDivisors@ n == Total@ antiDivisors@ EulerPhi@ n; k = 3; lst = {}; While[k < 10000001, If[ fQ@ k, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Jun 21 2014 *) CROSSREFS Cf. A000203, A066417, A230373, A033632. Sequence in context: A103853 A192160 A139202 * A125968 A147068 A147012 Adjacent sequences: A243993 A243994 A243995 * A243997 A243998 A243999 KEYWORD nonn AUTHOR Paolo P. Lava, Jun 18 2014 EXTENSIONS a(22)-a(25) from Robert G. Wilson v, Jun 21 2014 a(26)-a(34) from Hiroaki Yamanouchi, Sep 28 2015 STATUS approved

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Last modified June 17 03:50 EDT 2024. Contains 373432 sequences. (Running on oeis4.)