A335421 -id:A335421 - cp's OEIS frontend

A335420 a(n) = A000120(A163511(n)).

1, 1, 1, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 4, 2, 3, 1, 3, 4, 6, 2, 4, 3, 3, 2, 4, 4, 3, 2, 3, 3, 3, 1, 6, 3, 5, 4, 7, 6, 6, 2, 4, 4, 6, 3, 4, 3, 5, 2, 4, 4, 6, 4, 4, 3, 4, 2, 6, 3, 5, 3, 2, 3, 3, 1, 6, 6, 6, 3, 7, 5, 5, 4, 5, 7, 7, 6, 3, 6, 6, 2, 5, 4, 5, 4, 8, 6, 7, 3, 6, 4, 6, 3, 6, 5, 4, 2, 5, 4, 7, 4, 4, 6, 5, 4, 6

Offset: 0

Antti Karttunen, Jun 09 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A000079 (positions of ones), A000120, A001222, A163511, A335421, A335422.

Cf. also A323901, A334204.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A054429(n) = ((3<<#binary(n\2))-n-1);
A163511(n) = if(!n,1,A005940(1+A054429(n)));
A335420(n) = hammingweight(A163511(n));

from sympy import nextprime
def A335420(n):
    c, p, k = 1, 1, n
    while k:
        c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())
        k >>= s+1
    return (c*p).bit_count() # Chai Wah Wu, Jul 25 2023

a(n) = A000120(A163511(n)).
a(n) = A001222(A335422(n)).
a(n) = a(2n) = a(A000265(n)).
For all n >= 0, a(2^n) = 1.

A335422 a(n) = A005940(1+A163511(n)).

Original entry on oeis.org

2, 3, 5, 4, 7, 10, 9, 6, 11, 36, 21, 50, 25, 16, 15, 8, 13, 154, 225, 486, 55, 84, 147, 98, 49, 90, 81, 28, 35, 30, 27, 12, 17, 2500, 429, 8918, 1225, 1080, 9375, 840, 91, 2662, 495, 3750, 605, 220, 363, 1250, 121, 88, 525, 240, 625, 490, 99, 126, 77, 64, 105, 72, 125, 22, 45, 18, 19, 26950, 21609, 43350, 1105, 186340, 67881

Offset: 0

Antti Karttunen, Jun 09 2020

nonn

Permutation of natural numbers larger than one.

Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for sequences related to binary expansion of n

Cf. A001222, A005940, A054429, A163511, A335420, A335421.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429
A163511(n) = if(!n,1,A005940(1+A054429(n)))
A335422(n) = A005940(1+A163511(n));

a(n) = A005940(1+A163511(n)).
For all n >= 0, a(2^n) = A000040(2+n).
A001222(a(n)) = A335420(n).

cp's OEIS Frontend

A335420 a(n) = A000120(A163511(n)).

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