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.

A053470 a(n) is the cototient of n (A051953) iterated twice.

Original entry on oeis.org

0, 0, 0, 1, 0, 2, 0, 2, 1, 4, 0, 4, 0, 4, 1, 4, 0, 8, 0, 8, 3, 8, 0, 8, 1, 8, 3, 8, 0, 12, 0, 8, 1, 12, 1, 16, 0, 12, 7, 16, 0, 22, 0, 16, 9, 16, 0, 16, 1, 22, 1, 16, 0, 24, 7, 16, 9, 22, 0, 24, 0, 16, 9, 16, 1, 24, 0, 24, 5, 24, 0, 32, 0, 20, 11, 24, 1, 36, 0, 32, 9, 30, 0, 44, 9, 24, 1, 32, 0
Offset: 1

Views

Author

Labos Elemer, Jan 14 2000

Keywords

Comments

Iteration of A051953 is ended at fixed point 0. Analogous 2nd iterates for number of divisors (A000005) and Euler-Phi (A000010) are A036454 and A010554.

Examples

			n=50, n_1 = n - phi(n) = 50 - 20 = 30, n_2 = n_1 - Phi(n_1) = 30 - 8 = 22, so the 50th term is 22.

Links

Crossrefs

Cf. A051953, A000005, A000010, A036454, A010554.
Cf. A053471, A053472, A053473.

Programs

Formula

a(1) = 0; for n > 1, a(n) = A051953(A051953(n)).

A053472 a(n) is the cototient of n (A051953) iterated 4 times.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 4, 0, 4, 0, 4, 0, 8, 0, 4, 1, 4, 0, 4, 0, 8, 0, 4, 0, 8, 0, 4, 1, 8, 0, 8, 0, 4, 1, 4, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 16, 0, 8, 1, 12, 0, 16, 1, 8, 0, 8, 0, 16, 0, 8, 0, 8, 0, 8, 0, 8, 1, 16, 0, 16
Offset: 1

Views

Author

Labos Elemer, Jan 14 2000

Keywords

Comments

As iteration of A051953 progresses, powers of 2 may appear and it ends at fixed point 0. Analogous 4th iterates for A000005 or A000010 are A036452 and A049100.
It is assumed here that the value of A051953 at 0 is 0. - Antti Karttunen, Dec 22 2017

Examples

			n=50, n_1 = n - phi(n) = 50 - 20 = 30, n_2 = n_1 - Phi(n_1) = 30 - 8 = 22, n_3 = 22 - Phi(22) = 12, n_4 = n_3 - Phi(n_3) = 12 - 4 = 8 so the 50th term is 8.

Links

Crossrefs

Cf. A051953, A000005, A000010, A036452, A049100.
Cf. A053470, A053471, A053473.

Programs

A053473 a(n) is the cototient of n (A051953) iterated 5 times.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 2, 0, 4, 0, 4, 0, 2, 0, 2, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 8, 0, 8, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, 0, 4, 0, 4, 0, 8, 0, 8, 0, 4, 1
Offset: 1

Views

Author

Labos Elemer, Jan 14 2000

Keywords

Comments

As iteration of A051953 progresses, more and more powers of 2 and 0 appear. The fixed point is 0. Analogous 5th iterates for A000005 or A000010 are A036453 and A049107.
It is assumed here that the value of A051953 at 0 is 0. - Antti Karttunen, Dec 22 2017

Examples

			n=50, n_1 = n - phi(n) = 50 - 20 = 30, n_2 = n_1 - Phi(n_1) = 30 - 8 = 22, n_3 = 22 - Phi(22) = 12, n_4 = n_3 - Phi(n_3) = 12 - 4 = 8, n_5 = 8 - Phi(8) = 4 so the 50th term is 4.

Links

Crossrefs

Cf. A051953, A000005, A000010, A036453, A049107.
Cf. A053470, A053471, A053472.

Programs

Showing 1-3 of 3 results.

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