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A373361 a(n) = gcd(n, A276085(n)), where A276085 is the primorial base log-function.

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%I A373361 #9 Jun 02 2024 17:34:31
%S A373361 1,1,1,2,1,3,1,1,1,1,1,4,1,1,1,4,1,1,1,4,1,1,1,1,1,1,3,4,1,3,1,1,1,1,
%T A373361 1,6,1,19,1,1,1,3,1,4,5,1,1,6,1,1,1,4,1,1,1,1,1,1,1,10,1,1,1,2,1,3,1,
%U A373361 4,1,1,1,1,1,1,1,4,1,3,1,10,1,1,1,2,1,1,1,1,1,1,13,4,1,1,1,1,1,1,1,2,1,3,1,1,1
%N A373361 a(n) = gcd(n, A276085(n)), where A276085 is the primorial base log-function.
%H A373361 Antti Karttunen, <a href="/A373361/b373361.txt">Table of n, a(n) for n = 1..65537</a>
%H A373361 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%o A373361 (PARI)
%o A373361 A002110(n) = prod(i=1,n,prime(i));
%o A373361 A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
%o A373361 A373361(n) = gcd(n, A276085(n));
%Y A373361 Cf. A002110, A276085.
%Y A373361 Cf. A108269 (positions of even terms), A328981 (their characteristic function), A359794 (positions of odd terms), A359832 (their characteristic function, parity of terms).
%Y A373361 Cf. also A324198, A373145, A373362.
%K A373361 nonn
%O A373361 1,4
%A A373361 _Antti Karttunen_, Jun 02 2024