%I #17 Mar 08 2020 04:03:55

%S 1,3,7,81,13,525,19,19683,2401,1911,29,354375,37,6897,11011,43046721,

%T 43,4501875,53,2528253,22477,14703,61,2152828125,28561,32079,40353607,

%U 22532499,71,40465425,79,847288609443,58667,46569,71383,75969140625,89

%N If m = p_i^e_i, n=Product p_j^f_j, set G_m(n) = Product p_{j+i}^{f_j*e_i}; extend G_m to all m by multiplicativity; sequence gives a(n)=G_n(n).

%C m is a prime power iff a(m) is a prime power: A010055(a(A000961(n))) = 1 and A010055(a(A024619(n))) = 0. [_Reinhard Zumkeller_, Feb 16 2012]

%D From a puzzle proposed by _Marc LeBrun_.

%H Reinhard Zumkeller, <a href="/A045974/b045974.txt">Table of n, a(n) for n = 1..10000</a>

%e G_2(6) = 3*5, G_3(6) = 5*7, so G_6(6) = 3*5*5*7 = 525.

%o (Haskell)

%o a045974 n = g n n where

%o g x y = product [a000040 (a049084 pi + a049084 pj) ^ (ei * ej) |

%o (pi,ei) <- zip (a027748_row x) (a124010_row x),

%o (pj,ej) <- zip (a027748_row y) (a124010_row y)]

%o -- _Reinhard Zumkeller_, Feb 16 2012

%Y Cf. A027748, A124010, A049084, A000040.

%K nonn,nice,easy

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Naohiro Nomoto_, Mar 14 2001