A243061 Permutation of natural numbers, a composition of A241909 and A064216: a(n) = A064216(A241909(n)).

1, 2, 5, 3, 6, 13, 29, 4, 7, 47, 20, 25, 113, 95, 15, 11, 78, 23, 355, 158, 103, 267, 406, 89, 19, 1247, 17, 1237, 1577, 139, 660, 10, 221, 4363, 67, 38, 8179, 13109, 967, 393, 9266, 515, 21605, 4162, 28, 23601, 19578, 239, 43, 83, 987, 31247

Offset

1,2

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..1603

Index entries for sequences that are permutations of the natural numbers

Index entries for sequences computed from indices in prime factorization

Formula

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

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

Prog

(Scheme) (define (A243061 n) (A064216 (A241909 n)))
(PARI)
A064216(n) = A064989(n+n-1);
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) };
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));
A243061(n) = A064216(A241909(n)); \\ Antti Karttunen, Dec 10 2021

Crossrefs

Inverse permutation: A243062.

Cf. A064216, A241909, A243065-A243066.

Sequence in context: A111202 A194280 A163362 * A242911 A112486 A342659

Adjacent sequences: A243058 A243059 A243060 * A243062 A243063 A243064

Keyword

nonn

Author

Antti Karttunen, Jun 02 2014

Status

approved