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Primes together with 4.
7

%I #30 Jan 26 2024 13:31:16

%S 2,3,4,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,

%T 89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,

%U 179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277

%N Primes together with 4.

%C 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.

%C Numbers n whose sum of prime factors is n. - _Arkadiusz Wesolowski_, Jan 17 2012

%C Numbers n such that 2n has exactly four divisors. - _Wesley Ivan Hurt_, Jul 01 2013

%C Numbers n such that n^2 does not divide n!. - _Charles R Greathouse IV_, Nov 04 2013

%F a(n) = A046022(n+1). - _Omar E. Pol_, Nov 27 2012

%p 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:

%t Insert[Prime[Range[60]],4,3] (* _Harvey P. Dale_, Jan 26 2024 *)

%o (PARI) a(n)=if(n>3,prime(n-1),n+1) \\ _Charles R Greathouse IV_, Aug 26 2011

%Y Cf. A008472, A046022.

%K nonn,easy

%O 1,1

%A _Michel Lagneau_, Sep 04 2010

%E Switched comment and name. _Charles R Greathouse IV_, Nov 04 2013