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

1,1

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

Links

Table of n, a(n) for n=1..60.

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A008472, A046022.

Sequence in context: A211781 A348283 A046022 * A345899 A073019 A174291

Adjacent sequences: A175784 A175785 A175786 * A175788 A175789 A175790

Keyword

nonn,easy

Author

Michel Lagneau, Sep 04 2010

Extensions

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

Status

approved