login
A348509
a(n) is the numerator of the harmonic mean of the divisors of A003961(n).
1
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
1,2
FORMULA
a(n) = A099377(A003961(n)).
a(n) = A336845(n) / A336846(n).
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 *)
PROG
(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
CROSSREFS
Cf. A336848 (denominators).
Sequence in context: A101611 A268409 A182030 * A282141 A318321 A279510
KEYWORD
nonn,frac
AUTHOR
Antti Karttunen, Oct 31 2021
STATUS
approved