A348942 a(n) = A326042(n) / gcd(n, A326042(n)).

1, 1, 2, 11, 1, 1, 2, 3, 29, 1, 5, 11, 4, 1, 2, 49, 3, 29, 2, 11, 4, 5, 6, 1, 34, 2, 22, 11, 1, 1, 17, 55, 10, 3, 2, 319, 10, 1, 8, 3, 7, 2, 2, 5, 29, 3, 8, 49, 85, 17, 2, 11, 6, 11, 1, 3, 4, 1, 29, 11, 13, 17, 58, 1091, 4, 5, 4, 33, 4, 1, 31, 29, 3, 5, 68, 11, 10, 4, 10, 49, 469, 7, 12, 11, 3, 1, 2, 15, 25, 29, 8

Offset: 1

Author

Antti Karttunen, Nov 04 2021

Keywords

• nonn
• frac

Comments

Numerator of ratio A326042(n)/n. Ratio A326042(n)/n is multiplicative because both A326042 and A000027 are.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A005820, A007691, A046060, A064989, A326042, A348739, A348940, A348941 (denominators), A348943.

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_] := (sn = s2[n])/GCD[n, sn]; 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)));
A348942(n) = { my(u=A326042(n)); (u / gcd(n, u)); };

Formula

a(n) = A326042(n) / A348940(n) = A326042(n) / gcd(n, A326042(n)).

For all n >= 1, A348943(A064989(n)) = 1.