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

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

Author

Jamie Morken, May 24 2017

Keywords

• nonn

Comments

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)

Examples

			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)
		

Links

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

Crossrefs

Cf. A002110, A048863, A285784.

Programs

Mathematica

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 *)

PARI

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

Formula

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

Extensions

Edited by Michael De Vlieger, May 24 2017