cp's OEIS Frontend

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.

%I A122406 #34 Jun 09 2025 00:28:08
%S A122406 1,4,27,72,108,800,3125,6272,12500,21600,30375,36000,48600,84375,
%T A122406 121500,169344,225000,247808,337500,395136,750141,823543,857304,
%U A122406 1384448,3000564,3294172,6690816,19600000,22235661,24532992,37380096,37879808,53782400,59295096,88942644
%N 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.
%C A122406 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
%C A122406 From _Rémy Sigrist_, Oct 29 2017: (Start)
%C A122406 If gcd(a(i), a(j)) = 1, then a(i)*a(j) belongs to the sequence.
%C A122406 This sequence has similarities with A109297, where the prime exponents are a permutation of the prime indices. (End)
%H A122406 Alois P. Heinz, <a href="/A122406/b122406.txt">Table of n, a(n) for n = 1..1000</a>
%e A122406 2^5 * 3^3 * 5^2 = 21600, so 21600 is in the sequence. - corrected by _Jaroslav Krizek_, Jun 23 2011
%t A122406 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 *)
%o A122406 (PARI) is(n)=n=factor(n);vecsort(n[,1])==vecsort(n[,2]) \\ _Charles R Greathouse IV_, Jun 24 2011
%Y A122406 Subsequence of A054411, A054412, and A122405.
%Y A122406 Cf. A109297.
%K A122406 nonn
%O A122406 1,2
%A A122406 _Franklin T. Adams-Watters_, Sep 01 2006