A348940 a(n) = gcd(n, A326042(n)), where A326042 is multiplicative function A064989(sigma(A003961(n))).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Nov 04 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A326042, A348736, A348941, A348942.

Programs

Mathematica

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 *)

PARI

A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
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)};
A326042(n) = A064989(sigma(A003961(n)));
A348940(n) = gcd(n, A326042(n));

Formula

a(n) = gcd(n, A326042(n)).

a(n) = gcd(n, A348736(n)) = gcd(A326042(n), A348736(n));

a(n) = n / A348941(n) = A326042(n) / A348942(n).