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A074245 Numbers n such that sigma(n) is a harmonic number. 1

%I

%S 1,5,12,76,136,139,178,269,276,308,427,429,446,455,501,581,611,612,

%T 738,932,1576,1637,2952,2969,3184,3204,4647,4975,5400,5458,6199,7152,

%U 8816,9120,9180,9196,9272,9294,9504,9584,9720,9950,9960

%N Numbers n such that sigma(n) is a harmonic number.

%C Recall that n is harmonic if the harmonic mean of its divisors is an integer, i.e. if n * tau(n) / sigma(n) is an integer. (Tattersall, p. 147)

%D Tattersall, J. "Elementary Number Theory in Nine Chapters", Cambridge Univ. Press, 2001.

%H Amiram Eldar, <a href="/A074245/b074245.txt">Table of n, a(n) for n = 1..10000</a>

%e sigma(12) = 28 and 28 * tau(28) / sigma(28) = 28 * 6 / 56 = 3, an integer, so 12 is a term of the sequence.

%t isHarmonic[n_] := IntegerQ[n*DivisorSigma[0, n] / DivisorSigma[1, n]]; Select[Range[10^4], isHarmonic[DivisorSigma[1, # ]] &]

%Y Cf. A001599.

%K nonn

%O 1,2

%A _Joseph L. Pe_, Sep 19 2002

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Last modified August 4 08:25 EDT 2020. Contains 336201 sequences. (Running on oeis4.)