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Nonprimes k that are a totative of more than one primorial p_n# = A002110(n).
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%I #16 Oct 13 2018 12:33:59

%S 1,169,289,323,361,391,437,493,527,529,551,589,629,667,697,703,713,

%T 731,779,799,817,841,851,893,899,901,943,961,989,1003,1007,1037,1073,

%U 1081,1121,1139,1147,1159,1189,1207,1219,1241,1247,1271,1273,1333,1343,1349,1357,1363,1369,1387,1403,1411

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

%C From _Michael De Vlieger_, May 24 2017; corrected and edited by _M. F. Hasler_, Oct 04 2018: (Start)

%C 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).

%C Subset of A285784.

%C If considered as an irregular number triangle T(n,k), row lengths n < A048863(n).

%C (End)

%H M. F. Hasler, <a href="/A287391/b287391.txt">Table of n, a(n) for n = 1..1000</a>

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

%e From _Michael De Vlieger_, May 24 2017: (Start)

%e a(1) = 1 since 1 is coprime to all numbers.

%e 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)

%t 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 *)

%o (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

%Y Cf. A002110, A048863, A285784.

%K nonn

%O 1,2

%A _Jamie Morken_, May 24 2017

%E Edited by _Michael De Vlieger_, May 24 2017