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

5, 11, 13, 17, 23, 26, 29, 43, 47, 59, 61, 67, 73, 89, 101, 103, 107, 109, 113, 127, 146, 149, 151, 163, 167, 178, 179, 181, 191, 193, 223, 233, 241, 251, 257, 277, 311, 349, 353, 382, 401, 409, 419, 421, 433, 461, 466, 479, 487, 491, 509, 541, 557, 571, 573, 631, 641, 643, 659, 673, 719

Offset: 1

Author

Altug Alkan, Apr 29 2016

Keywords

• nonn

Comments

For n < 1000, there are 8 nonprime terms that are 26, 146, 178, 382, 466, 573, 802, 838.

4252 is the first term that has 3 prime divisors.

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

Examples

			5 is a term because A054640(5) = 6912 is not divisible by 5.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002110, A054640.

Programs

PARI

lista(nn) = for(n=1, nn, if(prod(i=1, n, prime(i)+1) % n != 0, print1(n, ", ")));

PARI

is(n)=prod(i=1, n, prime(i)+1)%n!=0 \\ Charles R Greathouse IV, Apr 29 2016

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

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