A114520 -id:A114520 - cp's OEIS frontend

A114521 a(n) = A008475(A114520(n)).

5, 7, 7, 11, 13, 11, 11, 19, 13, 13, 19, 17, 29, 31, 17, 23, 43, 19, 29, 31, 23, 61, 73, 41, 37, 83, 19, 47, 31, 67, 53, 103, 29, 17, 109, 37, 127, 71, 23, 139, 41, 151, 83, 31, 43, 181, 193, 131, 23, 101, 23, 199, 29, 41, 107, 19, 61, 43, 37, 113, 71, 229, 23, 67, 241

Offset: 1

Leroy Quet, Dec 05 2005

nonn

			24 (which is composite) is the sixth term of sequence A114520. 24 = 2^3 * 3 and 2^3 + 3 = 11 (which is prime). So a(6) = 11.

Cf. A008475, A114518, A114519, A114520, A047820.

f[n_] := Plus @@ Power @@@ FactorInteger[n]; f /@ Select[Select[Range[500], PrimeQ[f[ # ]] &], ! PrimeQ[ # ] &] (* Ray Chandler, Dec 07 2005 *)

A008475(n)=local(t);if(n<1,0,t=factor(n);sum(k=1,matsize(t)[1],t[k,1]^t[k,2])); for(i=1,900,if(!isprime(i)&&isprime(A008475(i)),print1(A008475(i),","))) (Herrgesell)

Extended by Ray Chandler and Lambert Herrgesell (zero815(AT)googlemail.com), Dec 07 2005

A114518 Numbers n such that A008475(n) is prime.

Original entry on oeis.org

2, 3, 5, 6, 7, 10, 11, 12, 13, 17, 18, 19, 22, 23, 24, 28, 29, 31, 34, 36, 37, 40, 41, 43, 47, 48, 52, 53, 54, 58, 59, 61, 67, 71, 72, 73, 76, 79, 82, 83, 88, 89, 97, 100, 101, 103, 107, 108, 109, 112, 113, 118, 127, 131, 137, 139, 142, 148, 149, 151, 157, 160, 162, 163

Offset: 1

Leroy Quet, Dec 05 2005

nonn

			24 = 2^3 * 3 and 2^3 + 3 = 11, which is prime. So 24 is included.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A008475, A114519, A114520, A114522.

f[n_] := Plus @@ Power @@@ FactorInteger[n]; Select[Range[165], PrimeQ[f[ # ]] &] (* Ray Chandler, Dec 07 2005 *)

A008475(n)=local(t);if(n<1,0,t=factor(n);sum(k=1,matsize(t)[1],t[k,1]^t[k,2])); for(i=1,500,if(isprime(A008475(i)),print1(i,","))) (Herrgesell)

Extended by Ray Chandler and Lambert Herrgesell (zero815(AT)googlemail.com), Dec 07 2005

cp's OEIS Frontend

A114521 a(n) = A008475(A114520(n)).

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