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

1,1

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

Links

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

Example

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

Prog

(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

Crossrefs

Cf. A002110, A054640.

Sequence in context: A288450 A346416 A371449 * A307390 A104110 A038936

Adjacent sequences: A272443 A272444 A272445 * A272447 A272448 A272449

Keyword

nonn

Author

Altug Alkan, Apr 29 2016

Status

approved