|
%I #26 Sep 08 2022 08:46:18
%S 9,2401,729,9765625,531441,45949729863572161,5559917313492231481,
%T 1471383076677527699142172838322885948765175969,
%U 10264895304762966931257013446474591264089923314972889033759201,230466617897195215045509519405933293401
%N a(n) is the smallest odd number k with prime sum of divisors such that tau(k) = n-th prime.
%C tau(n) = A000005(n) = the number of divisors of n.
%C For n >= 7; a(n) > A023194(10000) = 5896704025969.
%H Robert G. Wilson v, <a href="/A278914/b278914.txt">Table of n, a(n) for n = 2..66</a> (first 49 terms from Davin Park)
%F a(n) = A101636(n)^(prime(n)-1). - _Davin Park_, Dec 10 2016
%e a(2) = 9 because 9 is the smallest odd number with prime values of sum of divisors (sigma(9) = 13) such that tau(9) = 3 = 2nd prime.
%t A278914[n_] := NestWhile[NextPrime, 3, ! PrimeQ[Cyclotomic[Prime[n], #]] &]^(Prime[n] - 1); Array[A278914, 10, 2] (* _Davin Park_, Dec 28 2016 *)
%o (Magma) A278914:=func<n|exists(r){k:k in[1..10000000] | IsOdd(k) and IsPrime(SumOfDivisors(k)) and NumberOfDivisors(k) eq NthPrime(n)} select r else 0>; [A278914(n): n in[2..6]]
%o (PARI) a(n) = {my(k=1); while(! (isprime(sigma(k)) && isprime(p=numdiv(k)) && (primepi(p) == n)), k+=2); k;} \\ _Michel Marcus_, Dec 03 2016
%Y Cf. A000005, A000203, A278911, A278913.
%K nonn,more
%O 2,1
%A _Jaroslav Krizek_, Nov 30 2016
%E More terms from _Davin Park_, Dec 11 2016
| 