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.

A350317 Totient numbers k such that 5*k is a nontotient.

Original entry on oeis.org

1, 10, 18, 46, 58, 70, 78, 82, 102, 106, 110, 130, 136, 148, 166, 178, 190, 220, 222, 226, 238, 250, 262, 268, 270, 282, 292, 310, 316, 330, 342, 346, 358, 378, 382, 418, 430, 438, 442, 466, 478, 486, 490, 498, 502, 508, 522, 556, 562, 568, 586, 598, 606, 618
Offset: 1

Views

Author

Jianing Song, Dec 24 2021

Keywords

Examples

			10 is a term since 10 = phi(11) = phi(22), but phi(n) = 5*10 = 50 has no solution.
18 is a term since 18 = phi(19) = phi(27) = phi(38) = phi(54), but phi(n) = 5*18 = 90 has no solution.

Links

Crossrefs

Totient numbers k such that m*k is a nontotient: A350316 (m=3), this sequence (m=5), A350318 (m=7), A350319 (m=9), A350320 (m=10), A350321 (m=14).
Cf. A002202, A005277.

Programs

  • PARI
    isA350317(n) = istotient(n) && !istotient(5*n)

A350318 Totient numbers k such that 7*k is a nontotient.

Original entry on oeis.org

1, 2, 22, 44, 46, 52, 58, 82, 92, 102, 104, 110, 148, 162, 164, 172, 178, 190, 198, 222, 250, 262, 270, 282, 292, 296, 310, 342, 344, 356, 358, 366, 380, 382, 388, 442, 462, 466, 486, 490, 498, 500, 502, 506, 522, 524, 556, 562, 568, 570, 584, 586, 598, 620
Offset: 1

Views

Author

Jianing Song, Dec 24 2021

Keywords

Examples

			44 is a term since 44 = phi(69) = phi(92) = phi(138), but phi(n) = 7*44 = 308 has no solution.
52 is a term since 52 = phi(53) = phi(106), but phi(n) = 7*52 = 364 has no solution.

Links

Crossrefs

Totient numbers k such that m*k is a nontotient: A350316 (m=3), A350317 (m=5), this sequence (m=7), A350319 (m=9), A350320 (m=10), A350321 (m=14).
Cf. A002202, A005277.

Programs

  • PARI
    isA350318(n) = istotient(n) && !istotient(7*n)

A350319 Totient numbers k such that 9*k is a nontotient.

Original entry on oeis.org

1, 10, 46, 66, 78, 106, 126, 138, 150, 166, 178, 190, 210, 226, 262, 268, 270, 306, 346, 358, 366, 372, 378, 382, 418, 430, 442, 466, 478, 490, 506, 522, 546, 570, 586, 598, 606, 630, 646, 676, 682, 718, 726, 738, 750, 786, 810, 822, 826, 838, 882, 886, 906
Offset: 1

Views

Author

Jianing Song, Dec 24 2021

Keywords

Examples

			10 is a term since 10 = phi(11) = phi(22), but phi(n) = 9*10 = 90 has no solution.
46 is a term since 46 = phi(47) = phi(94), but phi(n) = 9*46 = 414 has no solution.

Links

Crossrefs

Totient numbers k such that m*k is a nontotient: A350316 (m=3), A350317 (m=5), A350318 (m=7), this sequence (m=9), A350320 (m=10), A350321 (m=14).
Cf. A002202, A005277.

Programs

  • PARI
    isA350319(n) = istotient(n) && !istotient(9*n)

A350320 Totient numbers k such that 10*k is a nontotient.

Original entry on oeis.org

110, 13310, 18260, 78980, 130460, 143660, 163460, 164780, 167420, 284900, 325160, 329780, 332420, 370700, 381260, 403700, 418220, 431420, 453860, 514580, 526460, 535700, 554180, 560780, 603020, 628100, 646580, 665060, 675620, 732380, 745580, 765380, 801020
Offset: 1

Views

Author

Jianing Song, Dec 24 2021

Keywords

Comments

10 is the smallest totient number that is not in A301587.
If 10*phi(m) is a nontotient, then m is divisible by 121 but not by 5, so every term is divisible by 110.
Proof. In the following cases, 10*phi(m) is a totient number:
(a) If m is not divisible by 11, then phi(11*m) = phi(11)*phi(m) = 10*phi(m).
(b) If m is divisible by 11 but not by 121 or 5, then phi((m/11)*125) = phi(m/11)*phi(125) = (phi(m)/10)*100 = 10*phi(m).
(c) If m is divisible by 5 but not by 2, then phi(4*5*m) = phi(4)*phi(5*m) = 2*(5*phi(m)) = 10*phi(m).
(d) If m is divisible by 5 and 2, then phi(10*m) = 10*phi(m).
So the only left case is that m is divisible by 121 but not by 5.

Examples

			110 is a term since 110 = phi(121) = phi(242), but phi(n) = 10*110 = 1100 has no solution.
13310 is a term since 13310 = phi(14641) = phi(29282), but phi(n) = 10*13310 = 133100 has no solution.

Links

Crossrefs

Totient numbers k such that m*k is a nontotient: A350316 (m=3), A350317 (m=5), A350318 (m=7), A350319 (m=9), this sequence (m=10), A350321 (m=14).
Cf. A002202, A005277, A301587.

Programs

  • PARI
    isA350320(n) = istotient(n) && !istotient(10*n)

A350321 Totient numbers k such that 14*k is a nontotient.

Original entry on oeis.org

1, 22, 46, 52, 82, 148, 172, 178, 190, 250, 262, 292, 310, 358, 366, 382, 388, 442, 466, 490, 502, 506, 556, 562, 568, 586, 598, 652, 658, 682, 718, 742, 772, 822, 852, 862, 910, 946, 982, 1090, 1102, 1150, 1162, 1186, 1210, 1222, 1278, 1282, 1306, 1366, 1372
Offset: 1

Views

Author

Jianing Song, Dec 24 2021

Keywords

Comments

14 is the smallest even nontotient.

Examples

			52 is a term since 52 = phi(53) = phi(106), but phi(n) = 14*52 = 728 has no solution.
172 is a term since 172 = phi(173) = phi(346), but phi(n) = 14*172 = 2408 has no solution.

Links

Crossrefs

Totient numbers k such that m*k is a nontotient: A350316 (m=3), A350317 (m=5), A350318 (m=7), A350319 (m=9), A350320 (m=10), this sequence (m=14).
Cf. A002202, A005277.

Programs

  • PARI
    isA350321(n) = istotient(n) && !istotient(14*n)
Showing 1-5 of 5 results.

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