A175787 Primes together with 4.

2, 3, 4, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277

Offset: 1

Author

Michel Lagneau, Sep 04 2010

Keywords

• nonn
• easy

Comments

sopf(n) is the sum of the distinct primes dividing n (A008472). Because sopf(n) = n if n is prime, this sequence is numbers n such that n^sopf(n) = sopf(n)^n.

Numbers n whose sum of prime factors is n. - Arkadiusz Wesolowski, Jan 17 2012

Numbers n such that 2n has exactly four divisors. - Wesley Ivan Hurt, Jul 01 2013

Numbers n such that n^2 does not divide n!. - Charles R Greathouse IV, Nov 04 2013

Crossrefs

Cf. A008472, A046022.

Programs

Maple

with(numtheory): digits:=200:nn:=200:for a from 1 to nn do: t1:=ifactors(a)[2]:t2:=sum(t1[i][1],i=1..nops(t1)) :if a^t2=t2^a then printf(`%d, `, a):else fi:od:

Mathematica

Insert[Prime[Range[60]],4,3] (* Harvey P. Dale, Jan 26 2024 *)

PARI

a(n)=if(n>3,prime(n-1),n+1) \\ Charles R Greathouse IV, Aug 26 2011

Formula

a(n) = A046022(n+1). - Omar E. Pol, Nov 27 2012

Extensions

Switched comment and name. Charles R Greathouse IV, Nov 04 2013