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.

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A351561 a(n) = n + d(n) - phi(n), where d is the number of divisors function, and phi is the Euler totient function.

Original entry on oeis.org

1, 3, 3, 5, 3, 8, 3, 8, 6, 10, 3, 14, 3, 12, 11, 13, 3, 18, 3, 18, 13, 16, 3, 24, 8, 18, 13, 22, 3, 30, 3, 22, 17, 22, 15, 33, 3, 24, 19, 32, 3, 38, 3, 30, 27, 28, 3, 42, 10, 36, 23, 34, 3, 44, 19, 40, 25, 34, 3, 56, 3, 36, 33, 39, 21, 54, 3, 42, 29, 54, 3, 60, 3, 42, 41, 46, 21, 62, 3, 58, 32, 46, 3, 72, 25, 48
Offset: 1

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Author

Antti Karttunen, Feb 21 2022

Keywords

Crossrefs

Cf. A000005, A000010 (phi), A008683 (mu), A020488 (fixed points), A051953, A063070.
Cf. also A055517.

Programs

  • Mathematica
    Array[# + DivisorSigma[0, #] - EulerPhi[#] &, 86] (* Michael De Vlieger, Feb 21 2022 *)
  • PARI
    A351561(n) = (n+numdiv(n)-eulerphi(n));

Formula

a(n) = A000005(n) + A051953(n) = n - A063070(n) = n + A000005(n) - A000010(n).
a(n) = Sum_{d|n} (1 + phi(d) - d*mu(n/d)). - Wesley Ivan Hurt, Jul 21 2025
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