A045974 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).

1, 3, 7, 81, 13, 525, 19, 19683, 2401, 1911, 29, 354375, 37, 6897, 11011, 43046721, 43, 4501875, 53, 2528253, 22477, 14703, 61, 2152828125, 28561, 32079, 40353607, 22532499, 71, 40465425, 79, 847288609443, 58667, 46569, 71383, 75969140625, 89

Offset

1,2

Comments

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]

References

From a puzzle proposed by Marc LeBrun.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

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

Prog

(Haskell)
a045974 n = g n n where
   g x y = product [a000040 (a049084 pi + a049084 pj) ^ (ei * ej) |
                    (pi, ei) <- zip (a027748_row x) (a124010_row x),
                    (pj, ej) <- zip (a027748_row y) (a124010_row y)]
-- Reinhard Zumkeller, Feb 16 2012

Crossrefs

Cf. A027748, A124010, A049084, A000040.

Sequence in context: A077793 A175236 A343763 * A001531 A219588 A219375

Adjacent sequences: A045971 A045972 A045973 * A045975 A045976 A045977

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Naohiro Nomoto, Mar 14 2001

Status

approved