A348825 - OEIS

A348825

Numbers k such that the denominator of the harmonic mean of the divisors of k is larger than k.

2, 4, 8, 9, 16, 25, 36, 64, 80, 81, 100, 104, 121, 128, 144, 208, 225, 256, 272, 289, 320, 324, 400, 484, 512, 529, 576, 625, 729, 841, 900, 1024, 1088, 1089, 1156, 1250, 1296, 1300, 1332, 1575, 1600, 1664, 1681, 1856, 1936, 2025, 2116, 2196, 2209, 2304, 2368

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OFFSET

1,1

COMMENTS

Numbers k such that A099378(k) > k.

This sequence is infinite. For example, if p is a prime of the form 6*k-1, then p^2 is a term.

2 is the only prime term, since the denominator of the harmonic mean of the divisors of an odd prime p is (p+1)/2 < p.

LINKS

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

EXAMPLE

2 is a term since the harmonic mean of the divisors of 2 is 4/3 and 3 > 2.

4 is a term since the harmonic mean of the divisors of 4 is 12/7 and 7 > 4.

MATHEMATICA

q[n_] := Denominator[DivisorSigma[0, n]/DivisorSigma[-1, n]] > n; Select[Range[2500], q]

PROG

(PARI) isok(k) = my(d=divisors(k)); (denominator(#d/sum(i=1, #d, 1/d[i])) > k); \\ Michel Marcus, Nov 01 2021

CROSSREFS

Cf. A007528, A099377, A099378.

Sequence in context: A204826 A241010 A354956 * A046678 A330606 A046680

Adjacent sequences: A348822 A348823 A348824 * A348826 A348827 A348828

KEYWORD

nonn

AUTHOR

Amiram Eldar, Nov 01 2021

STATUS

approved