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

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

Author

Altug Alkan, Aug 12 2016

Keywords

• nonn
• easy

Comments

From Robert Israel, Aug 12 2016: (Start)

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

For such m, sigma(m) = 1 + p + ... + p^k = (p*m-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)

Examples

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

Links

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

Crossrefs

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

Cf. A000040, A286095.

Programs

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

PARI

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

Formula

UNION of A000040 and A286095 (except for the term 2). - Bill McEachen, Jul 16 2024