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%I #13 Nov 15 2021 10:01:47
%S 1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,6,1,2,1,2,1,2,1,1,1,1,
%T 1,1,1,2,1,1,1,2,1,11,1,2,1,2,1,2,3,4,1,2,5,2,1,1,1,2,1,1,1,1,1,2,1,1,
%U 3,2,1,3,1,2,1,2,1,2,1,1,1,1,1,4,1,2,1,1,1,1,1,2,1,2,1,2,1,1,1,2,1,6,1,4,1
%N a(n) = gcd(n, A326042(n)), where A326042 is multiplicative function A064989(sigma(A003961(n))).
%H Antti Karttunen, <a href="/A348940/b348940.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = gcd(n, A326042(n)).
%F a(n) = gcd(n, A348736(n)) = gcd(A326042(n), A348736(n));
%F a(n) = n / A348941(n) = A326042(n) / A348942(n).
%t f1[2, e_] := 1; f1[p_, e_] := NextPrime[p, -1]^e; s[n_] := Times @@ f1 @@@ FactorInteger[n]; f[p_, e_] := s[((q = NextPrime[p])^(e + 1) - 1)/(q - 1)]; s2[1] = 1; s2[n_] := Times @@ f @@@ FactorInteger[n]; a[n_] := GCD[n, s2[n]]; Array[a, 100] (* _Amiram Eldar_, Nov 05 2021 *)
%o (PARI)
%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
%o A064989(n) = {my(f); 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 A326042(n) = A064989(sigma(A003961(n)));
%o A348940(n) = gcd(n, A326042(n));
%Y Cf. A326042, A348736, A348941, A348942.
%K nonn
%O 1,6
%A _Antti Karttunen_, Nov 04 2021
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