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 1-6 of 6 results.

A086571 a(1)=1, for n>1: a(n) = smallest divisor of n occurring earlier at most once.

Original entry on oeis.org

1, 1, 3, 2, 5, 2, 7, 4, 3, 5, 11, 4, 13, 7, 15, 8, 17, 6, 19, 10, 21, 11, 23, 6, 25, 13, 9, 14, 29, 10, 31, 8, 33, 17, 35, 9, 37, 19, 39, 20, 41, 14, 43, 22, 15, 23, 47, 12, 49, 25, 51, 26, 53, 18, 55, 28, 57, 29, 59, 12, 61, 31, 21, 16, 65, 22, 67, 34, 69, 35, 71, 18, 73
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 22 2003

Keywords

Comments

a(A086939(n)) = a(A086938(n)) = n. - Reinhard Zumkeller, Jul 24 2003

Examples

			a(p) = p for primes p>2;
divisor set of n=12: {1,2,3,4,6,12}, divisors occurring <12: 1=a(1)=a(2), 2=a(4)=a(6), 3=a(3)=a(9) and 4=a(8); as 4 occurs only once a(12)=4.

Links

Crossrefs

Cf. A086572, A086938, A086939.

Programs

  • Mathematica
    a = {1}; twice = {}; Do[nxt = Complement[Divisors[n], twice][[1]]; If[MemberQ[a, nxt], AppendTo[twice, nxt]]; AppendTo[a, nxt], {n, 2, 10}]; a (* Ivan Neretin, May 28 2015 *)

A086572 Solution to A086571(a(n))=A086571(n) and a(n)<>n.

Original entry on oeis.org

2, 1, 9, 6, 10, 4, 14, 12, 3, 5, 22, 8, 26, 7, 45, 32, 34, 24, 38, 30, 63, 11, 46, 18, 50, 13, 36, 42, 58, 20, 62, 16, 99, 17, 70, 27, 74, 19, 117, 100, 82, 28, 86, 66, 15, 23, 94, 60, 98, 25, 153, 78, 106, 72, 110, 84, 171, 29, 118, 48, 122, 31, 21, 80, 130, 44, 134
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 22 2003

Keywords

Comments

Well defined as each number occurs exactly twice in A086571;
a self-inverse permutation of natural numbers: a(a(n))=n.
A086938(n) = a(A086939(n)), A086939(n) = a(A086938(n)). - Reinhard Zumkeller, Jul 24 2003

Examples

			A086571(8)=4 and A086571(12)=4, therefore a(8)=12 and a(12)=8.

Links

A086957 Smallest m with A086956(m)=n.

Original entry on oeis.org

1, 4, 9, 16, 5, 18, 7, 32, 27, 50, 11, 72, 13, 28, 75, 64, 17, 108, 19, 100, 63, 44, 23, 192, 125, 52, 81, 196, 29, 180, 31, 128, 99, 68, 35, 288, 37, 76, 117, 200, 41, 294, 43, 176, 225, 92, 47, 384, 49, 250, 153, 208, 53, 486, 55, 392, 171, 116, 59, 420, 61
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 25 2003

Keywords

Comments

a(n) < A086958(n) < A086959(n), A086956(a(n))=A086956(A086958(n))=A086956(A086959(n));
n and A086956(n) are divisors of a(n);
A086960(a(n)) = A086958(n), A086960(A086959(n)) = a(n);
A086961(a(n)) = A086959(n), A086961(A086958(n)) = a(n);
A086962(a(n)) = a(n);
A086963(a(n)) = A086959(n), A086963(A086959(n)) = a(n);
A086964(a(n)) = A086958(n), A086964(A086958(n)) = a(n).

Crossrefs

Cf. A086938, A086939.

A086958 m such that A086956(m)=n and A086956(k)=n for exactly one kA086957(n)).

Original entry on oeis.org

2, 6, 12, 20, 10, 30, 14, 40, 45, 60, 22, 84, 26, 42, 90, 80, 34, 126, 38, 120, 147, 66, 46, 216, 150, 78, 135, 224, 58, 210, 62, 160, 132, 102, 245, 324, 74, 114, 156, 320, 82, 336, 86, 220, 315, 138, 94, 432, 98, 300, 204, 260, 106, 540, 110, 448, 228, 174
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 25 2003

Keywords

Comments

A086957(n) < a(n) < A086959(n), A086956(a(n))=A086956(A086957(n))=A086956(A086959(n));
n and A086956(n) are divisors of a(n);
A086960(A086957(n)) = a(n), A086960(a(n)) = A086959(n);
A086961(a(n)) = A086957(n), A086961(A086959(n)) = a(n);
A086962(a(n)) = A086959(n), A086962(A086959(n)) = a(n);
A086963(a(n)) = a(n);
A086964(A086957(n)) = a(n), A086964(a(n)) = A086957(n).

Crossrefs

Cf. A086938, A086939.

A086959 Greatest m with A086956(m)=n.

Original entry on oeis.org

3, 8, 15, 24, 25, 36, 21, 48, 54, 70, 33, 96, 39, 56, 105, 112, 51, 144, 57, 140, 168, 88, 69, 240, 175, 104, 162, 252, 87, 270, 93, 256, 165, 136, 280, 360, 111, 152, 195, 400, 123, 378, 129, 264, 405, 184, 141, 480, 343, 350, 255, 312, 159, 594, 275, 504
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 25 2003

Keywords

Comments

A086957(n) < A086958(n) < a(n), A086956(a(n))=A086956(A086957(n))=A086956(A086958(n));
n and A086956(n) are divisors of a(n);
A086960(A086958(n)) = a(n), A086960(a(n)) = A086957(n);
A086961(A086957(n)) = a(n), A086961(a(n)) = A086958(n);
A086962(A086958(n)) = a(n), A086962(a(n)) = A086958(n);
A086963(A086957(n)) = a(n), A086963(a(n)) = A086957(n);
A086964(a(n)) = a(n).

Crossrefs

Cf. A086938, A086939.

A086939 Greatest m with A086571(m) = n.

Original entry on oeis.org

2, 6, 9, 12, 10, 24, 14, 32, 36, 30, 22, 60, 26, 42, 45, 80, 34, 72, 38, 100, 63, 66, 46, 120, 50, 78, 108, 84, 58, 150, 62, 160, 99, 102, 70, 180, 74, 114, 117, 240, 82, 168, 86, 132, 225, 138, 94, 288, 98, 300, 153, 156, 106, 216, 110, 224, 171, 174, 118
Offset: 1

Views

Author

Reinhard Zumkeller, Jul 24 2003

Keywords

Comments

A086938(n) < a(n); A086571(a(n)) = A086571(A086938(n)) = n;
n and A086571 are divisors of a(n);
a(n) = A086572(A086938(n)), A086938(n) = A086572(a(n)).

Links

Showing 1-6 of 6 results.

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