A322827 -id:A322827 - cp's OEIS frontend

A324386 a(n) = A324383(A006068(n)).

1, 1, 2, 1, 2, 2, 2, 1, 4, 4, 4, 2, 2, 6, 6, 1, 2, 4, 8, 4, 4, 6, 12, 2, 8, 6, 10, 6, 22, 10, 8, 1, 4, 4, 6, 2, 8, 6, 8, 4, 6, 12, 14, 2, 16, 10, 16, 2, 8, 16, 4, 6, 14, 8, 24, 6, 30, 18, 20, 6, 26, 18, 26, 1, 6, 8, 8, 4, 12, 12, 6, 8, 12, 14, 18, 4, 20, 20, 20, 4, 16, 16, 8, 12, 28, 16, 10, 12, 22, 26, 14, 12, 34, 20, 22, 2, 12

Offset: 0

Antti Karttunen, Feb 27 2019

nonn

This is most likely equal to A276150(A086141(n)), apart from the different offset used in A086141.

The same comments about the parity of terms as in A324383 and A324387 apply also here, except here 1's occur at positions given by 2^k - 1.

Cf. A002110, A006068, A025487, A086141, A276150, A322827, A324342, A324382.

Cf. also A324383, A324387 (permutations of this sequence) and A324380, A324390.

A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ From A006068
A276150(n) = { my(s=0,m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };
A322827(n) = if(!n,1,my(bits = Vecrev(binary(n)), rl=1, o = List([])); for(i=2,#bits,if(bits[i]==bits[i-1], rl++, listput(o,rl))); listput(o,rl); my(es=Vecrev(Vec(o)), m=1); for(i=1,#es,m *= prime(i)^es[i]); (m));
A324383(n) = A276150(A322827(n));
A324386(n) = A324383(A006068(n));

a(n) = A324383(A006068(n)) = A276150(A322827(A006068(n))).

a(A000225(n)) = 1 for all n.

A329887 a(0) = 1, a(1) = 2; for n > 1, if n is even, then a(n) = 2*a(n/2), and if n is odd, a(n) = A283980(a((n-1)/2)).

Original entry on oeis.org

1, 2, 4, 6, 8, 36, 12, 30, 16, 216, 72, 900, 24, 180, 60, 210, 32, 1296, 432, 27000, 144, 5400, 1800, 44100, 48, 1080, 360, 6300, 120, 1260, 420, 2310, 64, 7776, 2592, 810000, 864, 162000, 54000, 9261000, 288, 32400, 10800, 1323000, 3600, 264600, 88200, 5336100, 96, 6480, 2160, 189000, 720, 37800, 12600, 485100, 240

Offset: 0

Antti Karttunen, Dec 24 2019

nonn

			This irregular table can be represented as a binary tree. Each child to the left is obtained by doubling the parent, and each child to the right is obtained by applying A283980 to the parent:
                                     1
                                     |
                  ...................2...................
                 4                                       6
       8......../ \........36                 12......../ \........30
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
  16      216         72      900         24      180         60       210
etc.
A329886 is the mirror image of the same tree.

Antti Karttunen, Table of n, a(n) for n = 0..8192

Permutation of A025487.
Cf. A054429, A108951, A163511, A283980, A329900.
Cf. also A322827, A329886.

{1}~Join~Nest[Append[#1, If[EvenQ@ #2, 2 #1[[#2/2]], (Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[# == 1])*2^IntegerExponent[#, 2] &[#1[[(#2 - 1)/2]] ]]] & @@ {#, Length@ # + 1} &, {2}, 55] (* Michael De Vlieger, Dec 29 2019 *)

A283980(n) = {my(f=factor(n)); prod(i=1, #f~, my(p=f[i, 1], e=f[i, 2]); if(p==2, 6, nextprime(p+1))^e)}; \\ From A283980
A329887(n) = if(n<2,1+n,if(n%2,A283980(A329887(n\2)),2*A329887(n/2)));

a(0) = 1, a(1) = 2; for n > 1, if n is odd, a(n) = A283980(a((n-1)/2)), and if n is even, then a(n) = 2*a(n/2).
a(n) = A108951(A163511(n)).
a(2^n) = 2^(1+n). [And all the terms following after a(2^n) are > 2^(1+n).]
For n >= 1, a(n) = A329886(A054429(n)).

cp's OEIS Frontend

A324386 a(n) = A324383(A006068(n)).

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