A306952 -id:A306952 - cp's OEIS frontend

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

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

Amiram Eldar, Mar 07 2020

nonn

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

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Nontotient.
Wikipedia, Nontotient.

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

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

A333101 Numbers k such that both k and k + 2 are noncototients (A005278).

Original entry on oeis.org

50, 170, 266, 290, 344, 518, 532, 534, 650, 686, 722, 730, 872, 962, 1036, 1158, 1166, 1332, 1394, 1462, 1464, 1586, 1634, 1682, 1804, 1864, 1922, 1946, 1970, 2034, 2072, 2074, 2116, 2134, 2262, 2314, 2316, 2318, 2330, 2420, 2534, 2598, 2666, 2668, 2772, 2822

Offset: 1

Amiram Eldar, Mar 07 2020

nonn

			50 is a term since both 50 and 52 are noncototients.

Eric Weisstein's World of Mathematics, Noncototient.
Wikipedia, Noncototient.

Cf. A005278, A072296, A231964, A306952, A333100.

nmax = 3000; cototientQ[n_?EvenQ] := (x = n; While[test = x - EulerPhi[x] == n ; Not[test || x > 2*nmax], x++]; test); cototientQ[n_?OddQ] = True; nonc = Select[Range[nmax], !cototientQ[#]&]; nonc[[Flatten[Position[Differences[nonc], 2]]]] (* after Jean-François Alcover at A005278 *)

A363295 Numbers k such that k and k+20 are consecutive unitary weird numbers (A064114).

Original entry on oeis.org

34121990, 34428290, 34766810, 34936070, 38014970, 38152010, 39506090, 39844610, 41400170, 42044990, 42552770, 42584990, 43769810, 46276490, 46308710, 47155010, 47324270, 47461310, 49016870, 49153910, 49323170, 49661690, 49863170, 50540210, 51015770, 51354290, 53079110

Offset: 1

Amiram Eldar, May 26 2023

nonn

Conjecture: All the unitary weird numbers are of the form 20*k + 10, and thus 20 is the least gap between consecutive unitary weird numbers (verified for the 16326260 unitary weird numbers below 10^10).

			34121990 is a term since 34121990 = A064114(53235) and 34122010 = 34121990 + 20 = A064114(53236) are consecutive unitary weird numbers.

Amiram Eldar, Table of n, a(n) for n = 1..17846 (terms below 10^10)

Cf. A064114, A306952, A363296.

cp's OEIS Frontend

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

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A333101 Numbers k such that both k and k + 2 are noncototients (A005278).

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Mathematica

A363295 Numbers k such that k and k+20 are consecutive unitary weird numbers (A064114).

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