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A008478
Integers of the form Product p_j^k_j = Product k_j^p_j; p_j in A000040.
11
1, 4, 16, 27, 72, 108, 432, 800, 3125, 6272, 12500, 21600, 30375, 50000, 84375, 121500, 169344, 225000, 247808, 337500, 486000, 750141, 823543, 1350000, 1384448, 3000564, 3294172, 6690816, 12002256, 13176688, 19600000, 22235661, 37380096, 37879808, 59295096, 88942644
OFFSET
1,2
COMMENTS
Fixed points of A008477.
a(3) = 16 is the only term of the form p^q with p <> q. - Bernard Schott, Mar 28 2021
EXAMPLE
16 = 2^4 = 4^2.
27 = 3^3.
108 = 2^2*3^3.
6272 = 2^7*7^2.
121500 = 2^2 * 3^5*5^3.
MATHEMATICA
f[n_] := Product[{p, e} = pe; e^p, {pe, FactorInteger[n]}];
Reap[For[n = 1, n <= 10^8, n++, If[f[n] == n, Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Mar 29 2021 *)
PROG
(PARI) for(n=2, 10^8, if(n==prod(i=1, omega(n), component(component(factor(n), 2), i)^component(component(factor(n), 1), i)), print1(n, ", ")))
CROSSREFS
Some subsequences: p_i^p_i (A051674), Product_i {p_i^p_i} (A048102), Product_(j,k)(p_j^p_k * p_k^p_j) with p_j < p_k (A082949) (see examples).
Sequence in context: A361078 A072653 A368107 * A201009 A111260 A067688
KEYWORD
nonn
EXTENSIONS
More terms from David W. Wilson
a(34)-a(36) from Jean-François Alcover, Mar 29 2021
STATUS
approved