%I #8 Jul 19 2021 01:25:55

%S 1,2,3,4,5,3,7,1,1,5,11,3,13,7,5,1,17,1,19,5,7,11,23,3,1,13,3,7,29,5,

%T 31,2,11,17,7,1,37,19,13,1,41,1,43,11,1,23,47,1,1,1,17,13,53,9,11,7,

%U 19,29,59,1,61,31,1,4,13,11,67,17,23,1,71,3,73,37,25,19,1,13,79,1,1,41,83,1,17,43,29,11,89

%N a(n) = gcd(n, A346098(n)).

%C Only powers of primes (A000961) occur as terms. A346100 lists the exponents.

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

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

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

%F a(n) = gcd(n, A346098(n)) = gcd(n, A064989(A319626(A324886(n)))).

%o (PARI)

%o A064989(n) = { my(f = factor(n)); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };

%o A319626(n) = (n / gcd(n, A064989(n)));

%o A346099(n) = gcd(n, A064989(A319626(A324886(n)))); \\ Rest of program in A324886.

%Y Cf. A000961, A064989, A319626, A324886, A346095, A346096, A346097, A346098, A346100.

%Y Cf. A346090 (positions of ones).

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 07 2021