A348509 a(n) is the numerator of the harmonic mean of the divisors of A003961(n).

1, 3, 5, 27, 7, 5, 11, 27, 75, 21, 13, 45, 17, 11, 35, 405, 19, 225, 23, 189, 55, 39, 29, 9, 49, 17, 125, 99, 31, 35, 37, 729, 65, 57, 77, 2025, 41, 23, 85, 189, 43, 55, 47, 27, 525, 29, 53, 675, 363, 147, 19, 51, 59, 125, 13, 99, 115, 93, 61, 315, 67, 111, 275, 5103, 119, 65, 71, 513, 29, 77, 73, 405, 79, 41, 245

Offset: 1

Author

Antti Karttunen, Oct 31 2021

Keywords

• nonn
• frac

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003961, A099377, A336845, A336846.

Cf. A336848 (denominators).

Programs

Mathematica

f[p_, e_] := (e + 1)*(pn = NextPrime[p])^e*(pn - 1)/(pn^(e + 1) - 1); a[1] = 1; a[n_] := Numerator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* Amiram Eldar, Oct 31 2021 *)

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A099377(n) = { my(d=divisors(n)); numerator(#d/sum(k=1, #d, 1/d[k])); }; \\  From A099377
A348509(n) = A099377(A003961(n));

Formula

a(n) = A099377(A003961(n)).

a(n) = A336845(n) / A336846(n).