A342462 Sum of digits when A329886(n) is written in primorial base, where A329886 is the primorial inflation of Doudna-tree.

1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 6, 4, 6, 4, 2, 4, 1, 2, 6, 4, 10, 6, 6, 4, 8, 12, 10, 8, 22, 4, 8, 2, 1, 2, 6, 4, 6, 2, 6, 2, 18, 10, 8, 6, 18, 12, 16, 4, 26, 16, 24, 8, 20, 14, 4, 6, 26, 16, 14, 8, 30, 6, 8, 4, 1, 2, 6, 4, 14, 12, 12, 8, 18, 12, 24, 4, 8, 12, 14, 4, 24, 20, 28, 20, 26, 16, 16, 12, 32, 26, 24, 14, 28, 16

Offset: 0

Author

Antti Karttunen, Mar 15 2021

Keywords

• nonn

Comments

From David A. Corneth's Feb 27 2019 comment in A276150 follows that the only odd terms in this sequence are 1's occurring at 0 and at two's powers.

Subsequences starting at each n = 2^k are slowly converging towards A329886: 1, 2, 6, 4, 30, 12, 36, 8, 210, 60, 180, 24, etc.. Compare also to the behaviors of A324342 and A342463.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8192
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to primorial base

Crossrefs

Cf. A001222, A005940, A108951, A276150, A329886, A342456, A342457, A342461, A342463, A342464.

Cf. also A324342, A324383, A324387, A324888.

Programs

PARI

A342462(n) = bigomega(A342456(n)); \\ Other code as in A342456.

PARI

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)};
A329886(n) = if(n<2,1+n,if(!(n%2),A283980(A329886(n/2)),2*A329886(n\2)));
A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
A342462(n) = A276150(A329886(n));

Formula

a(n) = A001222(A342456(n)) = A001222(A342457(n)).

a(n) = A276150(A329886(n)) = A324888(A005940(1+n)).

a(n) >= A342461(n).

For n >= 0, a(2^n) = 1.