cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A248795 Numbers k such that 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, 5, 15, 255, 65535, 2200694, 2619705, 6372794, 40588485, 76466985, 81591194, 118018094, 206569605, 470542485, 525644385, 726638834, 791937614, 971122514, 991172805, 1268457014, 1384822005, 1613055045, 1709460753, 1861556654, 1872619665, 2507927414, 2659263945
Offset: 1

Views

Author

Jaroslav Krizek, Nov 19 2014

Keywords

Comments

Numbers k such that A029940(k) = A029940(k+1).
4294967295 is in this sequence.

Examples

			15 is in the sequence because A029940(15) = A029940(16) = 64.

Crossrefs

Cf. A000010, A019434, A029940, A248796.

Programs

  • Magma
    [n: n in [1..100000] | (&*[EulerPhi(d): d in Divisors(n)]) eq (&*[EulerPhi(d): d in Divisors(n+1)])];
  • Mathematica
    a248795[n_Integer] := Select[Range[n],
Product[EulerPhi[i], {i, Divisors[#]}] ==
Product[EulerPhi[j], {j, Divisors[# + 1]}] &]; a248795[10^5] (* Michael De Vlieger, Nov 30 2014 *)
  • PARI
    lista(nn) = {d = divisors(1); vcur = prod(k=1, #d, eulerphi(d[k])); for (n=2, nn, d = divisors(n); vnext = prod(k=1, #d, eulerphi(d[k])); if (vnext == vcur, print1(n-1, ", ")); vcur = vnext;);} \\ Michel Marcus, Nov 23 2014

Formula

a(n) = A248796(n) - 2.

Extensions

a(7)-a(9) from Michel Marcus, Nov 21 2014
a(10)-a(20) from Michel Marcus, Nov 23 2014
More terms from Jinyuan Wang, Jul 27 2025

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

Views

Author

Jaroslav Krizek, Nov 21 2014

Keywords

Comments

Primes p such that A029940(p-2) = A029940(p-1).
First 5 known terms of Fermat primes (A019434) are terms of this sequence.

Examples

			Prime 17 is in the sequence because A029940(15) = A029940(16) = 64.

Crossrefs

Subsequence of A248796. Supersequence of A247203.
Cf. A000010, A019434, A029940, A248795.

Programs

  • Magma
    [n: n in [3..100000] |  IsPrime(n) and (&*[EulerPhi(d): d in Divisors(n-2)]) eq (&*[EulerPhi(d): d in Divisors(n-1)])];

Formula

A029940(a(n)) = a(n) - 1.

Extensions

a(8)-a(9) from Jinyuan Wang, Jul 27 2025

A247203 Primes p such that phi(p-2) = phi(p-1) and simultaneously 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, 17, 257, 65537, 991172807, 1872619667, 4081364447
Offset: 1

Views

Author

Jaroslav Krizek, Nov 25 2014

Keywords

Comments

Primes p such that A000010(p-2) = A000010(p-1) and simultaneously A029940(p-2) = A029940(p-1).
The first 5 known Fermat primes (A019434) are terms of this sequence.

Examples

			17 is in the sequence because phi(15) = phi(16) = 8 and simultaneously Product_{d|15} phi(d) = Product_{d|16} phi(d) = 64.

Crossrefs

Subsequence of A247164 and A248796.
Cf. A000010, A029940.

Programs

  • Magma
    [p: p in PrimesInInterval(3, 10^7) | (&*[EulerPhi(d): d in Divisors(p-2)]) eq (&*[EulerPhi(d): d in Divisors(p-1)]) and EulerPhi(p-2) eq EulerPhi(p-1)];
  • Magma
    [n: n in [A248796(n)] | IsPrime(n) and EulerPhi(n-2) eq EulerPhi(n-1)];
  • Magma
    [n: n in [A247164(n)] | IsPrime(n) and EulerPhi(n-2) eq EulerPhi(n-1)];

Extensions

a(7)-a(8) from Jinyuan Wang, Jul 27 2025
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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