A348509 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..75.

Index entries for sequences computed from indices in prime factorization

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

A348509(n) = A099377(A003961(n));

CROSSREFS

Cf. A003961, A099377, A336845, A336846.

Cf. A336848 (denominators).

Sequence in context: A101611 A268409 A182030 * A282141 A318321 A279510

Adjacent sequences: A348506 A348507 A348508 * A348510 A348511 A348512

KEYWORD

nonn,frac

AUTHOR

Antti Karttunen, Oct 31 2021

STATUS

approved