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 1-5 of 5 results.

A333102 Numbers k such that both k and k + 2 are both nontotients and noncototients (A058763).

Original entry on oeis.org

532, 722, 872, 962, 1394, 1586, 1682, 1922, 2072, 2116, 2262, 2314, 2316, 2534, 2822, 2946, 3026, 3052, 3112, 3172, 3174, 3176, 3426, 3474, 3486, 3626, 3686, 3892, 4082, 4146, 4184, 4234, 4292, 4526, 4528, 4578, 4610, 4628, 5066, 5250, 5252, 5546, 5962, 5964, 6104
Offset: 1

Views

Author

Amiram Eldar, Mar 07 2020

Keywords

Examples

			532 is a term since both 532 and 534 are both nontotients and noncototients.

Links

Crossrefs

Intersection of A333100 and A333101.
Cf. A005277, A005278, A058763, A063512, A072296.

A058817 Even cototient numbers.

Original entry on oeis.org

0, 2, 4, 6, 8, 12, 14, 16, 18, 20, 22, 24, 28, 30, 32, 36, 38, 40, 42, 44, 46, 48, 54, 56, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 88, 90, 92, 94, 96, 98, 102, 104, 106, 108, 110, 112, 114, 118, 120, 124, 126, 128, 132, 136, 138, 140, 142, 144, 148, 150, 152
Offset: 1

Views

Author

Labos Elemer, Jan 04 2001

Keywords

Examples

			88 is here because it is the cototient of 120: 88 = 120-phi(120) = 120-32 = 88.

Links

Crossrefs

Cf. A000010, A051953, A063742, A005277, A005278, A002202, A058763.

Programs

  • Mathematica
    With[{max = 300}, Union@ Select[Table[n - EulerPhi[n], {n, 1, max^2}], # < max && EvenQ[#] &]] (* Amiram Eldar, Jan 12 2024 *)

Formula

Even terms of A063742.

Extensions

Offset corrected by Donovan Johnson, Nov 17 2013
a(1) = 0 inserted by Amiram Eldar, Jan 12 2024

A058825 Numbers which are both totients and cototients.

Original entry on oeis.org

1, 2, 4, 6, 8, 12, 16, 18, 20, 22, 24, 28, 30, 32, 36, 40, 42, 44, 46, 48, 54, 56, 60, 64, 66, 70, 72, 78, 80, 82, 84, 88, 92, 96, 102, 104, 106, 108, 110, 112, 120, 126, 128, 132, 136, 138, 140, 144, 148, 150, 156, 160, 162, 164, 166, 168, 176, 178, 180, 184, 190
Offset: 1

Views

Author

Labos Elemer, Jan 04 2001

Keywords

Examples

			24 is here because 24 = phi(72) = 44-phi(44) = 44-20 = cototient(44).

Links

Crossrefs

Cf. A000010, A051953, A005277, A005278, A002020, A058763.

Formula

Intersection(A002202, A051953).

Extensions

Offset corrected by Donovan Johnson, Nov 17 2013

A058826 Even cototient numbers which are nontotients.

Original entry on oeis.org

14, 38, 62, 68, 74, 76, 90, 94, 98, 114, 118, 124, 142, 152, 158, 174, 182, 188, 194, 214, 230, 234, 236, 242, 246, 248, 254, 258, 278, 284, 286, 302, 304, 308, 314, 318, 322, 334, 338, 350, 354, 364, 370, 374, 376, 390, 398, 402, 406, 410, 414, 422, 426
Offset: 1

Views

Author

Labos Elemer, Jan 04 2001

Keywords

Examples

			14 is a nontotient number but it is cototient of 26: 14 = 26 - phi(26).

Links

Crossrefs

Cf. A000010, A051953, A005277, A005278, A002020, A058763, A058817.

Formula

Intersection(A058817, A005277).

A058827 Totients which are not cototients.

Original entry on oeis.org

10, 52, 58, 100, 116, 130, 172, 222, 232, 260, 268, 292, 310, 344, 346, 366, 372, 466, 490, 520, 536, 546, 562, 580, 584, 652, 688, 732, 772, 786, 808, 906, 932, 940, 980, 1018, 1038, 1068, 1072, 1108, 1160, 1168, 1192, 1210, 1300, 1332, 1360, 1372, 1376
Offset: 1

Views

Author

Labos Elemer, Jan 04 2001

Keywords

Examples

			10, the smallest noncototient number, is the totient of 11.

Links

Crossrefs

Cf. A000010, A051953, A005277, A005278, A002020, A058763.

Formula

Intersection(noncototients=A005278, A002202=totients).

Extensions

More terms from Don Reble, Nov 28 2001
Offset corrected by Donovan Johnson, Nov 17 2013
Showing 1-5 of 5 results.

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