A008367 -id:A008367 - cp's OEIS frontend

A306097 Terms of A121707 not in A267999.

697, 1241, 1247, 1271, 1513, 2057, 2201, 2329, 2501, 2873, 3053, 3131, 3683, 3689, 3961, 4015, 4061, 4141, 4777, 4859, 4991, 5321, 5921, 5963, 6137, 6851, 6953, 7421, 7769, 7781, 7957, 8471, 8711, 8857, 9017, 9211, 9271, 9401, 9641, 9673, 10217, 10277, 10489, 10795, 11033, 11501

Offset: 1

M. F. Hasler, following remarks from Tomasz Ordowski, Oct 03 2018

nonn

Numbers n such that gcd(n, 2^n-2) > 1 and gcd(n, b^n-b) = 1 for some b > 2, b < n.
Or: Numbers n such that gcd(n, 2^n-2) > 1 and for every prime factor p of n, p-1 does not divide n-1.
2057 is the first term not in A008367, nor in A287391. - M. F. Hasler, Oct 04 2018

			The smallest element of this sequence is a(1) = 697 = 17*41.

M. F. Hasler, Table of n, a(n) for n = 1..10000

Cf. A121707, A267999.

is(n,p)={for(i=1, #p=factor(n)[,1], (n-1)%(p[i]-1)||return); gcd(n, lift(Mod(2,n)^n-2))>1}

A121707 \ A267999.

A287391 Nonprimes k that are a totative of more than one primorial p_n# = A002110(n).

Original entry on oeis.org

1, 169, 289, 323, 361, 391, 437, 493, 527, 529, 551, 589, 629, 667, 697, 703, 713, 731, 779, 799, 817, 841, 851, 893, 899, 901, 943, 961, 989, 1003, 1007, 1037, 1073, 1081, 1121, 1139, 1147, 1159, 1189, 1207, 1219, 1241, 1247, 1271, 1273, 1333, 1343, 1349, 1357, 1363, 1369, 1387, 1403, 1411

Offset: 1

Jamie Morken, May 24 2017

nonn

From Michael De Vlieger, May 24 2017; corrected and edited by M. F. Hasler, Oct 04 2018: (Start)
Let p_n# = A002110(n). This sequence lists 1 and composite numbers p_n# < k < p_(n+1)# for all positive n such that least_prime_factor(k) > p_(n+2).
Subset of A285784.
If considered as an irregular number triangle T(n,k), row lengths n < A048863(n).
(End)

			From _Michael De Vlieger_, May 24 2017: (Start)
a(1) = 1 since 1 is coprime to all numbers.
169 is in the sequence since it is coprime to p_4# = 210 and p_5# = 2310 yet less than both, however prime(6) = 13 divides 169 thus it is not a totative of p_6# or any larger primorial. (End)

M. F. Hasler, Table of n, a(n) for n = 1..1000

Cf. A002110, A048863, A285784.

MapIndexed[Select[Range @@ #1, Function[k, Function[f, And[If[First@ #2 == 1, k == 1 || Total[f[[All, -1]]] > 1, Total[f[[All, -1]]] > 1], CoprimeQ[Last@ #1, k], f[[1, 1]] != Prime[First@ #2 + 1]]]@ FactorInteger[k]]] &, Partition[FoldList[#1 #2 &, 1, Prime@ Range@ 5], 2, 1]] // Flatten (* Michael De Vlieger, May 24 2017 *)

is(n,f=if(n>1,factor(n)[,1][1],4),P=1)={n!=f&&forprime(p=2,precprime(f-1)-1,n%p||return;(P*=p)>n&&return(1))} \\ M. F. Hasler, Oct 04 2018

For 2 < n <= 108, a(n) = A008367(n-2); for 109 <= n < 120, a(n) = A008367(n). - M. F. Hasler, Oct 04 2018

Edited by Michael De Vlieger, May 24 2017

cp's OEIS Frontend

A306097 Terms of A121707 not in A267999.

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