A122406 Numbers of the form Product_i p_i^e_i, where the p_i are distinct primes and the e_i are a permutation of the p_i.

1, 4, 27, 72, 108, 800, 3125, 6272, 12500, 21600, 30375, 36000, 48600, 84375, 121500, 169344, 225000, 247808, 337500, 395136, 750141, 823543, 857304, 1384448, 3000564, 3294172, 6690816, 19600000, 22235661, 24532992, 37380096, 37879808, 53782400, 59295096, 88942644

Offset: 1

Author

Franklin T. Adams-Watters, Sep 01 2006

Keywords

• nonn

Comments

Numbers m such that if m = Product_i [p_i^e_i] then m = Product_i [e_i * (p_i^(e_i - 1))]. Example: 21600 = 2^5 * 3^3 * 5^2 = 5*2^4 * 3*3^2 * 2*5^1. - Jaroslav Krizek, Jun 23 2011

From Rémy Sigrist, Oct 29 2017: (Start)

If gcd(a(i), a(j)) = 1, then a(i)*a(j) belongs to the sequence.

This sequence has similarities with A109297, where the prime exponents are a permutation of the prime indices. (End)

Examples

			2^5 * 3^3 * 5^2 = 21600, so 21600 is in the sequence. - corrected by _Jaroslav Krizek_, Jun 23 2011
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A054411, A054412, and A122405.

Cf. A109297.

Programs

Mathematica

Clear[f, seq]; f[sub_] := f[sub] = (Times @@ (sub^#) & ) /@ Permutations[sub]; seq[0] = {1}; seq[k_] := seq[k] = Union[seq[k - 1], f /@ Subsets[Prime /@ Range[17], {k}] // Flatten // Union // Select[#, # <= 6836638277409177600000 &] &]; seq[k = 1]; While[nterms = Length[seq[k]]; nterms < 1000, k++; Print["nterms = ", nterms]]; seq[k] (* Jean-François Alcover, Dec 09 2013, using Alois P. Heinz's data *)

PARI

is(n)=n=factor(n);vecsort(n[,1])==vecsort(n[,2]) \\ Charles R Greathouse IV, Jun 24 2011