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Exponential of Mangoldt function M(n) applied to primorial base exp-function: a(n) = A014963(A276086(n)).
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%I #10 Jan 14 2024 12:37:52

%S 1,2,3,1,3,1,5,1,1,1,1,1,5,1,1,1,1,1,5,1,1,1,1,1,5,1,1,1,1,1,7,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,1,1,1,1,

%U 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1

%N Exponential of Mangoldt function M(n) applied to primorial base exp-function: a(n) = A014963(A276086(n)).

%C Also LCM-transform of A276086, because A276086 has the S-property explained in the comments of A368900.

%H Antti Karttunen, <a href="/A369010/b369010.txt">Table of n, a(n) for n = 0..30030</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = A014963(A276086(n)).

%F For n > 0, a(n) = lcm {1..A276086(n)} / lcm {1..A276086(n-1)}.

%o (PARI)

%o A014963(n) = { ispower(n, , &n); if(isprime(n), n, 1); };

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A369010(n) = A014963(A276086(n));

%o (PARI)

%o up_to = 510511; \\ = 1+A002110(7);

%o LCMtransform(v) = { my(len = length(v), b = vector(len), g = vector(len)); b[1] = g[1] = 1; for(n=2,len, g[n] = lcm(g[n-1],v[n]); b[n] = g[n]/g[n-1]); (b); };

%o v369010 = LCMtransform(vector(up_to,n,A276086(n-1)));

%o A369010(n) = v369010[1+n];

%Y Cf. A014963, A060735 (positions of terms > 1), A276086, A368900.

%K nonn

%O 0,2

%A _Antti Karttunen_, Jan 14 2024