A113570 - OEIS

A113570

Consider the function f(k) in A110545, i.e., the smallest positive integer j such that k divides either the numerator or the denominator of the reduced Harmonic number H(j). This sequence lists numbers k where f(k)=k.

1, 2, 4, 8, 9, 16, 27, 32, 64, 81, 125, 128, 243, 256, 343, 512, 625, 729, 1024, 2048, 2187, 2197, 2401, 3125, 4096, 4913, 6561, 6859, 8192, 12167, 14641, 15625, 16384, 16807, 19683, 24389, 28561, 29791, 32768, 50653, 59049, 65536, 68921, 78125, 79507, 83521

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OFFSET

1,2

COMMENTS

If p^e is present then p^(e+1) is also. The generators are: 2^0, 3^2, 5^3, 7^3, 11^4, 13^3, 17^3, 19^3, 23^3, 29^3, 31^3, ...

Conjecture: only prime powers are present (A025475) in addition to 1 and 2. Thus this sequence would be a proper subset of A000961.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..57

MATHEMATICA

f[n_] := Block[{h = k = 1}, While[ !IntegerQ[ Numerator[h]/n] && !IntegerQ[ Denominator[h]/n], k++; h = h + 1/k]; k]; t = Table[f[n], {n, 10000}]; Select[ Range[10000], t[[ # ]] == # &]

CROSSREFS

Cf. A110545.

Sequence in context: A330606 A046680 A331992 * A065391 A161792 A111261

Adjacent sequences: A113567 A113568 A113569 * A113571 A113572 A113573

KEYWORD

nonn

AUTHOR

Leroy Quet and Robert G. Wilson v, Sep 29 2005

STATUS

approved