A295417 - OEIS

%I #30 Oct 19 2021 07:23:21

%S 1,2,3,4,5,6,7,8,9,10,11,18,13,14,15,16,17,12,19,50,21,22,23,54,25,26,

%T 27,98,29,30,31,32,33,34,35,36,37,38,39,250,41,42,43,242,75,46,47,162,

%U 49,20,51,338,53,24,55,686,57,58,59,450,61,62,147,64,65,66

%N Self-inverse permutation of natural numbers: in prime factorization of n replace each positive prime exponent e with max + min - e, where max = A051903(n) and min = A051904(n).

%C This sequence was inspired by A293448.

%C This sequence first differs from A293448 at n = 42: a(42) = 42 whereas A293448(42) = 70.

%C a(A293448(n)) = A293448(a(n)) for any n > 0.

%C a(n) = n iff n belongs to A072774.

%C f(n) = f(a(n)) for any n > 0 and f in { A001221, A006530, A007947, A020639, A051903, A051904 }.

%C The lines visible in the logarithmic scatterplot of the sequence seems to correspond to integer sets where the function A062760 is constant (see logarithmic scatterplot in Links section).

%H Rémy Sigrist, <a href="/A295417/b295417.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A295417/a295417.png">Colored logarithmic scatterplot of the first 1000000 terms</a> (where the color is function of A062760(n))

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = A007947(n)^(A051903(n) + A051904(n)) / n.

%e For n = 1620:

%e - 1620 = 2^2 * 3^4 * 5,

%e - A051903(1620) = 4 and A051904(1620) = 1,

%e - a(1620) = 2^(4+1-2) * 3^(4+1-4) * 5^(4+1-1) = 2^3 * 3 * 5^4 = 15000.

%o (PARI) a(n) = { my(f=factor(n)); if(#f~<=1, return(n), my(mi=vecmin(f[,2]), ma=vecmax(f[,2])); return(prod(i=1, #f~, f[i,1]^(ma+mi-f[i,2])))) }

%Y Cf. A001221, A006530, A007947, A020639, A051903, A051904, A062760, A072774 (fixed points), A293448.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Nov 22 2017