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

%I A342462 #23 Apr 09 2021 09:21:36
%S A342462 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,
%T A342462 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,
%U A342462 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
%N A342462 Sum of digits when A329886(n) is written in primorial base, where A329886 is the primorial inflation of Doudna-tree.
%C A342462 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.
%C A342462 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.
%H A342462 Antti Karttunen, <a href="/A342462/b342462.txt">Table of n, a(n) for n = 0..8192</a>
%H A342462 Antti Karttunen, <a href="/A342462/a342462.txt">Data supplement: n, a(n) computed for n = 0..65537</a>
%H A342462 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A342462 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A342462 a(n) = A001222(A342456(n)) = A001222(A342457(n)).
%F A342462 a(n) = A276150(A329886(n)) = A324888(A005940(1+n)).
%F A342462 a(n) >= A342461(n).
%F A342462 For n >= 0, a(2^n) = 1.
%o A342462 (PARI) A342462(n) = bigomega(A342456(n)); \\ Other code as in A342456.
%o A342462 (PARI)
%o A342462 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)};
%o A342462 A329886(n) = if(n<2,1+n,if(!(n%2),A283980(A329886(n/2)),2*A329886(n\2)));
%o A342462 A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
%o A342462 A342462(n) = A276150(A329886(n));
%Y A342462 Cf. A001222, A005940, A108951, A276150, A329886, A342456, A342457, A342461, A342463, A342464.
%Y A342462 Cf. also A324342, A324383, A324387, A324888.
%K A342462 nonn
%O A342462 0,4
%A A342462 _Antti Karttunen_, Mar 15 2021