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A272446 Numbers n such that A054640(n) is not divisible by n.

%I A272446 #18 Jan 06 2023 22:07:38
%S A272446 5,11,13,17,23,26,29,43,47,59,61,67,73,89,101,103,107,109,113,127,146,
%T A272446 149,151,163,167,178,179,181,191,193,223,233,241,251,257,277,311,349,
%U A272446 353,382,401,409,419,421,433,461,466,479,487,491,509,541,557,571,573,631,641,643,659,673,719
%N A272446 Numbers n such that A054640(n) is not divisible by n.
%C A272446 For n < 1000, there are 8 nonprime terms that are 26, 146, 178, 382, 466, 573, 802, 838.
%C A272446 4252 is the first term that has 3 prime divisors.
%C A272446 Note that 4252 is of the form 4p where p is prime, as are the next 42 such terms; the 44th, 213438, is 2*3*35573. Similarly, the first terms with 4 prime divisors are 1000024, 5921528, 6060344, 7355576, 10427512, 11727704, all of the form 8p with p prime. - _Charles R Greathouse IV_, Jan 06 2023
%H A272446 Charles R Greathouse IV, <a href="/A272446/b272446.txt">Table of n, a(n) for n = 1..10000</a>
%e A272446 5 is a term because A054640(5) = 6912 is not divisible by 5.
%o A272446 (PARI) lista(nn) = for(n=1, nn, if(prod(i=1, n, prime(i)+1) % n != 0, print1(n, ", ")));
%o A272446 (PARI) is(n)=prod(i=1, n, prime(i)+1)%n!=0 \\ _Charles R Greathouse IV_, Apr 29 2016
%o A272446 (PARI) is(n)=my(m=Mod(1,n)); forprime(p=2,prime(n), m*=p+1; if(m==0, return(0))); 1 \\ _Charles R Greathouse IV_, Apr 29 2016
%o A272446 (PARI) is(n,f=factor(n),r=prime(n))=for(i=1,#f~, my(p=f[i,1],e=f[i,2]); forprimestep(q=p-1,r,p, e-=valuation(q+1,p); if(e<=0, break)); if(e>0, return(1))); 0 \\ _Charles R Greathouse IV_, Jan 03 2023
%Y A272446 Cf. A002110, A054640.
%K A272446 nonn
%O A272446 1,1
%A A272446 _Altug Alkan_, Apr 29 2016