A275938 Numbers n such that d(n) is prime while sigma(n) is not prime (where d(n) = A000005(n) and sigma(n) = A000203(n)).

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277

Offset

1,1

Comments

From Robert Israel, Aug 12 2016: (Start)

d(n) is prime iff n = p^k where p is prime and k+1 is prime.

For such n, sigma(n) = 1+p+...+p^k = (pn-1)/(p-1).

The sequence contains 2^(q-1) for q in A054723,

3^(q-1) for q prime but not in A028491,

5^(q-1) for q prime but not in A004061,

7^(q-1) for q prime but not in A004063, etc.

In particular, it contains all odd primes. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

49 is a term because A000005(49) = 3 is prime while sigma(49) = 57 is not.

Maple

N:= 1000: # to get all terms <= N
P:= select(isprime, {2, seq(p, p=3..N, 2)}):
fp:= proc(p) local q, res;
  q:= 2;
  res:= NULL;
  while p^(q-1) <= N do
     if not isprime((p^q-1)/(p-1)) then res:= res, p^(q-1) fi;
     q:= nextprime(q);
  od;
  res;
end proc:
sort(convert(map(fp, P), list)); # Robert Israel, Aug 12 2016

Prog

(PARI) lista(nn) = for(n=1, nn, if(isprime(numdiv(n)) && !isprime(sigma(n)), print1(n, ", ")));

Crossrefs

Cf. A000005, A000203, A004061, A004063, A009087, A023194, A028491.

Sequence in context: A338483 A318871 A330225 * A093893 A056912 A075763

Adjacent sequences: A275935 A275936 A275937 * A275939 A275940 A275941

Keyword

nonn,easy

Author

Altug Alkan, Aug 12 2016

Status

approved