A348414 -id:A348414 - cp's OEIS frontend

A348656 Numbers with record values of the denominator of the harmonic mean of their unitary divisors.

1, 2, 4, 8, 16, 26, 32, 50, 58, 64, 98, 106, 122, 128, 178, 194, 202, 218, 226, 242, 250, 256, 346, 362, 386, 394, 458, 466, 482, 512, 698, 706, 722, 746, 778, 794, 802, 818, 842, 866, 898, 914, 922, 1018, 1024, 1402, 1418, 1466, 1514, 1522, 1538, 1546, 1594, 1618

Offset: 1

Amiram Eldar, Oct 28 2021

nonn

The corresponding record values are 1, 3, 5, 9, 17, 21, 33, 39, 45, 65, 75, ... (see the link for more values).

			The first 8 terms of A103340 are 1, 3, 2, 5, 3, 1, 4 and 9. The record values, 1, 3, 5 and 9, occur at 1, 2, 4 and 8, the first 4 terms of this sequence.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Amiram Eldar, Table of n, a(n), A103340(a(n)) for n = 1..10000

The unitary version of A348414.

Cf. A103339, A103340.

f[p_, e_] := 2/(1 + p^(-e)); d[n_] := Denominator[Times @@ f @@@ FactorInteger[n]]; dm = 0; s = {}; Do[dn = d[n]; If[dn > dm, dm = dn; AppendTo[s, n]], {n, 1, 1000}]; s

A348847 Numbers k where the ratios A099378(k)/k reach a record value.

Original entry on oeis.org

1, 2, 4, 8, 16, 36, 144, 576, 900, 3600, 14400, 32400, 129600, 435600, 6969600, 8643600, 34574400, 77792400, 311169600, 2498000400, 2800526400, 7779240000, 9992001600, 22482003600

Offset: 1

Amiram Eldar, Nov 02 2021

Are there nonsquare terms in this sequence that are larger than 8?

			The first 4 ratios A099378(k)/k, for k = 1 to 4, are 1, 3/2, 2/3 and 7/4. The record values occur at k = 1, 2 and 4, the first 3 terms of this sequence.

Cf. A099377, A099378, A348414.

r[n_] := Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]]/n; s = {}; rm = 0; Do[If[(r1 = r[n]) > rm, rm = r1; AppendTo[s, n]], {n, 1, 5*10^5}]; s

cp's OEIS Frontend

A348656 Numbers with record values of the denominator of the harmonic mean of their unitary divisors.

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