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a(n) = gcd(n, A332449(n)), where A332449(n) = A005940(1+(3*A156552(n))).
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%I #10 Apr 13 2022 16:49:40

%S 1,2,3,2,5,2,7,2,3,2,11,2,13,2,3,2,17,2,19,10,3,2,23,6,5,2,3,14,29,2,

%T 31,2,3,2,5,2,37,2,3,10,41,6,43,22,3,2,47,6,7,2,3,26,53,6,5,14,3,2,59,

%U 2,61,2,21,2,5,2,67,34,3,2,71,6,73,2,3,38,7,2,79,10,3,2,83,2,5,2,3,22,89,2,7,46,3,2,5,6

%N a(n) = gcd(n, A332449(n)), where A332449(n) = A005940(1+(3*A156552(n))).

%H Antti Karttunen, <a href="/A353270/b353270.txt">Table of n, a(n) for n = 1..16384</a>

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

%F a(n) = gcd(n, A332449(n)) = gcd(n, A005940(1+(3*A156552(n)))).

%F a(n) = n / A353271(n) = A332449(n) / A353272(n).

%o (PARI)

%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };

%o A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };

%o A332449(n) = A005940(1+(3*A156552(n)));

%o A353270(n) = gcd(n, A332449(n));

%Y Cf. A005940, A156552, A332449, A353271, A353272, A353274.

%K nonn

%O 1,2

%A _Antti Karttunen_, Apr 09 2022