A369028 Exponential of Mangoldt function permuted by A253563.

1, 2, 2, 3, 2, 1, 3, 5, 2, 1, 1, 1, 3, 1, 5, 7, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 7, 11, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 7, 1, 11, 13, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,2

Comments

Also LCM-transform of A253563 (when viewed as an offset-1 sequence), because A253563 has the S-property explained in the comments of A368900.

Links

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for sequences related to binary expansion of n

Formula

a(n) = A014963(A253563(n)).

a(1) = 0, and for n > 0, a(n) = lcm {1..A253563(n)} / lcm {1..A253563(n-1)}. [See comments]

Prog

(PARI)
A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A253550(n) = if(1==n, 1, (n/prime(A061395(n)))*prime(1+A061395(n)));
A253560(n) = if(1==n, 1, (n*prime(A061395(n))));
A253563(n) = if(n<2, (1+n), if(!(n%2), A253560(A253563(n/2)), A253550(A253563((n-1)/2))));
A369028(n) = A014963(A253563(n));

Crossrefs

Cf. A014963, A054429, A368900, A369029, A369030, A369053.

Sequence in context: A242266 A239617 A304737 * A092565 A021452 A093420

Adjacent sequences: A369025 A369026 A369027 * A369029 A369030 A369031

Keyword

nonn

Author

Antti Karttunen, Jan 12 2024

Status

approved