OFFSET
1,3
COMMENTS
a(A000040(n)) = n, hence all natural numbers appear in this sequence.
a(2n) = n.
It appears that a(35) = 12 is the only instance where a composite index yields a larger value than any smaller index. Checked to 10^7. - Charles R Greathouse IV, Jul 30 2016
LINKS
Paul Tek, Table of n, a(n) for n = 1..10000
Paul Tek, Perl program for this sequence
FORMULA
Multiplicative, with a(prime(i)^j) = i^a(j).
EXAMPLE
The number 9967 is the 1228th prime number.
Hence a(9967) = 1228.
The recursive prime factorization of 31250 is 2*5^(2*3).
The numbers 2, 3 and 5 are respectively the 1st, 2nd and 3rd prime numbers.
Hence a(31250) = a(2*5^(2*3)) = 1*3^(1*2) = 9.
MATHEMATICA
a[1] = 1; a[p_?PrimeQ] := a[p] = PrimePi[p]; a[n_] := a[n] = Times @@ (PrimePi[#[[1]]]^a[#[[2]]]& /@ FactorInteger[n]); Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jun 07 2013 *)
PROG
(Perl) see link.
(Haskell)
a225395 n = product $ zipWith (^)
(map a049084 $ a027748_row n) (map a225395 $ a124010_row n)
-- Reinhard Zumkeller, May 10 2013
(PARI) a(n)=if(n<3, return(1)); my(f=factor(n)); prod(i=1, #f~, primepi(f[i, 1])^a(f[i, 2])) \\ Charles R Greathouse IV, Jul 30 2016
CROSSREFS
KEYWORD
nonn,mult,nice
AUTHOR
Paul Tek, May 06 2013
STATUS
approved