A340091 -id:A340091 - cp's OEIS frontend

A340092 Carmichael numbers k for which A053575(k) [the odd part of phi] does not divide k-1.

1729, 2821, 15841, 29341, 41041, 52633, 63973, 75361, 101101, 115921, 126217, 172081, 188461, 252601, 278545, 294409, 314821, 334153, 340561, 399001, 488881, 512461, 530881, 552721, 656601, 658801, 670033, 748657, 825265, 838201, 852841, 997633, 1024651, 1033669, 1050985, 1082809, 1152271, 1193221, 1461241, 1569457

Offset: 1

Antti Karttunen, Dec 31 2020

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000
Index entries for sequences related to Carmichael numbers.

Complement of A339869 in A002997.
Subsequence of A340091.
Cf. A002322, A053575.

odd[n_] := n/2^IntegerExponent[n, 2]; Select[Range[1, 10^6, 2], CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] && !Divisible[# - 1, odd @ EulerPhi[#]] &] (* Amiram Eldar, Dec 31 2020 *)

A000265(n) = (n>>valuation(n, 2));
A002322(n) = lcm(znstar(n)[2]);
isA340092(n) = ((n>1)&&!isprime(n)&&(!((n-1)%A002322(n)))&&(0<((n-1)%A000265(eulerphi(n)))));

A340151 Setwise difference A340150 \ A340076.

Original entry on oeis.org

445, 527, 935, 1207, 1577, 1595, 1705, 1711, 2101, 2145, 2201, 2507, 3245, 3315, 4895, 6045, 6631, 6931, 7511, 8371, 9707, 9845, 10189, 10295, 10505, 11023, 11895, 12137, 12194, 13145, 13571, 13845, 14101, 14245, 15042, 15281, 16235, 16643, 17355, 17701, 18559, 19567, 20119, 20865, 22703, 23347, 25123, 26581, 27101, 27695

Offset: 1

Antti Karttunen, Dec 30 2020

nonn

Positions k where A340149(k) = 1, but A340075(k) > 1.

Setwise difference A340150 \ A340076.
Cf. A340091 (gives the same terms prime shifted once and sorted into ascending order).
Cf. A340075, A340149.

isA340151(n) = ((1!=A340075(n))&&(1==A340149(n))); \\ Uses code from both A340075 and A340149

cp's OEIS Frontend

A340092 Carmichael numbers k for which A053575(k) [the odd part of phi] does not divide k-1.

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