A351083 - OEIS

%I #29 Jun 18 2024 16:19:13

%S 0,1,1,1,2,1,1,7,8,1,1,1,2,1,1,5,16,1,3,1,10,1,1,1,4,25,1,1,2,1,1,1,2,

%T 1,17,5,12,1,1,13,2,1,1,1,4,5,1,1,2,1,25,1,4,1,3,5,2,1,1,1,2,1,1,7,4,

%U 1,1,1,2,1,7,1,24,1,1,5,2,7,1,1,80,1,1,1,14,5,1,1,8,1,3,91,4,1,1,1,2,1,49,1,4

%N a(n) = gcd(n, A003415(A276086(n))), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

%H Antti Karttunen, <a href="/A351083/b351083.txt">Table of n, a(n) for n = 0..65537</a>

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

%F a(n) = gcd(n, A327860(n)) = gcd(n, A003415(A276086(n))).

%F a(n) = A373145(A276086(n)). - _Antti Karttunen_, Jun 18 2024

%t Array[Block[{i, m, n = #, p}, m = i = 1; While[n > 0, p = Prime[i]; m *= p^Mod[n, p]; n = Quotient[n, p]; i++]; GCD[#, If[m < 2, 0, m Total[#2/#1 & @@@ FactorInteger[m]]]]] &, 101, 0] (* _Michael De Vlieger_, Feb 04 2022 *)

%o (PARI)

%o A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };

%o A351083(n) = gcd(n, A327860(n));

%Y Cf. A003415, A276086, A324198, A327860, A328572, A351080, A351084, A351087 (fixed points), A354823 (Dirichlet inverse), A373145, A373599 (indices of multiples of 3 in this sequence).

%Y Cf. A166486 (a(n) mod 2, parity of terms, see comment in A327860).

%Y Cf. also A345000.

%K nonn,base,easy

%O 0,5

%A _Antti Karttunen_, Feb 03 2022