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.

Previous Showing 11-13 of 13 results.

A333100 Even numbers k such that both k and k + 2 are nontotients (A005277).

Original entry on oeis.org

74, 122, 152, 186, 234, 242, 244, 246, 284, 302, 338, 362, 374, 402, 404, 410, 412, 426, 434, 470, 472, 482, 494, 514, 516, 530, 532, 548, 572, 594, 602, 608, 626, 666, 668, 678, 722, 728, 746, 752, 788, 802, 804, 842, 844, 866, 868, 870, 872, 890, 892, 914, 942
Offset: 1

Views

Author

Amiram Eldar, Mar 07 2020

Keywords

Examples

			74 is a term since both 74 and 76 are nontotients.

Links

Crossrefs

Cf. A005277, A063512, A231964, A306952, A333101.

Programs

  • PARI
    forstep(k=2, 100, 2, if(!istotient(k) && !istotient(k+2), print1(k,", ")))

A072296 Least number starting a chain of exactly n consecutive even integers that do not have cototient-inverses.

Original entry on oeis.org

10, 50, 532, 2314, 4628, 22578, 115024, 221960, 478302, 3340304, 22527850, 117335136, 1118736102, 1564578508, 6121287812, 7515991946
Offset: 1

Views

Author

Robert G. Wilson v, Jul 12 2002

Keywords

Comments

If the strong Goldbach conjecture (every even number>6 is the sum of at least 2 distinct primes p and q) is true, sequence contains only even values. Since p*q-phi(p*q)=p+q-1 and then every odd number can be expressed as x-phi(x). - Benoit Cloitre, Mar 03 2002.

Examples

			Neither 50 nor 52 have cototient-inverses and since 50 is the first of the two and the least number with this property, a(2) = 50.

Crossrefs

Cf. A005278, A051953, A063512, A063740.

Programs

  • Mathematica
    a = Table[0, {5*10^7}]; Do[b = n - EulerPhi[n]; If[ b < 5*10^7 + 1, a[[b/2]]++ ], {n, 2, 615437100}] (* used to find a(7) *) Do[ If[ a[[n]] == a[[n + 1]] == a[[n + 2]] == a[[n + 3]] == a[[n + 4]] == a[[n + 5]] == a[[n + 6]] == 0, Print[n]], {n, 1, 10^6}]

Extensions

a(12)-a(14) from Donovan Johnson, Jun 23 2010
a(15)-a(16) from Donovan Johnson, Jun 03 2013

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.
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.