A243061 - OEIS

%I #12 Dec 12 2021 16:08:13

%S 1,2,5,3,6,13,29,4,7,47,20,25,113,95,15,11,78,23,355,158,103,267,406,

%T 89,19,1247,17,1237,1577,139,660,10,221,4363,67,38,8179,13109,967,393,

%U 9266,515,21605,4162,28,23601,19578,239,43,83,987,31247

%N Permutation of natural numbers, a composition of A241909 and A064216: a(n) = A064216(A241909(n)).

%C This is A241909-conjugate of A243065. Please see the comments at the latter sequence.

%H Antti Karttunen, <a href="/A243061/b243061.txt">Table of n, a(n) for n = 1..1603</a>

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

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A064216(A241909(n)).

%F a(n) = A241909(A243065(A241909(n))).

%o (Scheme) (define (A243061 n) (A064216 (A241909 n)))

%o (PARI)

%o A064216(n) = A064989(n+n-1);

%o A064989(n) = { my(f = factor(n)); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f) };

%o A241909(n) = if(1==n||isprime(n),2^primepi(n),my(f=factor(n),h=1,i,m=1,p=1,k=1); while(k<=#f~, p = nextprime(1+p); i = primepi(f[k,1]); m *= p^(i-h); h = i; if(f[k,2]>1, f[k,2]--, k++)); (p*m));

%o A243061(n) = A064216(A241909(n)); \\ _Antti Karttunen_, Dec 10 2021

%Y Inverse permutation: A243062.

%Y Cf. A064216, A241909, A243065-A243066.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 02 2014