A248796
Numbers k such that Product_{d|(k-2)} phi(d) = Product_{d|(k-1)} phi(d) where phi(x) = Euler totient function (A000010).
Original entry on oeis.org
3, 5, 7, 17, 257, 65537, 2200696, 2619707, 6372796, 40588487, 76466987, 81591196, 118018096, 206569607, 470542487, 525644387, 726638836, 791937616, 971122516, 991172807, 1268457016, 1384822007, 1613055047, 1709460755, 1861556656, 1872619667, 2507927416, 2659263947
Offset: 1
17 is in the sequence because A029940(15) = A029940(16) = 64.
A247164
Primes p such that Product_{d|(p-2)} phi(d) = Product_{d|(p-1)} phi(d) where phi(x) = Euler totient function (A000010).
Original entry on oeis.org
3, 5, 7, 17, 257, 65537, 991172807, 1872619667, 4081364447
Offset: 1
Prime 17 is in the sequence because A029940(15) = A029940(16) = 64.
A247174
Numbers k such that phi(k) = phi(k+1) and simultaneously Product_{d|k} phi(d) = Product_{d|(k+1)} phi(d) where phi(x) = Euler totient function (A000010).
Original entry on oeis.org
1, 3, 15, 255, 65535, 2200694, 2619705, 6372794, 40588485, 76466985, 81591194, 118018094, 206569605, 470542485, 525644385, 726638834, 791937614, 971122514, 991172805
Offset: 1
15 is in the sequence because phi(15) = phi(16) = 8 and simultaneously Product_{d|15} phi(d) = Product_{d|(15+1)} phi(d) = 64.
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[n: n in [1..100000] | (&*[EulerPhi(d): d in Divisors(n)]) eq (&*[EulerPhi(d): d in Divisors(n+1)]) and EulerPhi(n) eq EulerPhi(n+1)]
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[n: n in [A248795(n)] | EulerPhi(n) eq EulerPhi(n+1)]
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a247174[n_Integer] := Module[{a001274, a248795},
a001274[m_] := Select[Range[m], EulerPhi[#] == EulerPhi[# + 1] &];
a248795[m_] :=
Select[Range[m],
Product[EulerPhi[i], {i, Divisors[#]}] ==
Product[EulerPhi[j], {j, Divisors[# + 1]}] &];
Intersection[a001274[n], a248795[n]]] (* Michael De Vlieger, Dec 01 2014 *)
Showing 1-3 of 3 results.
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