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A090945 Harmonic numbers (A001599) which are not perfect (A000396). 4
1, 140, 270, 672, 1638, 2970, 6200, 8190, 18600, 18620, 27846, 30240, 32760, 55860, 105664, 117800, 167400, 173600, 237510, 242060, 332640, 360360, 539400, 695520, 726180, 753480, 950976, 1089270, 1421280, 1539720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, B2.

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..77

T. Goto and S. Shibata, All numbers whose positive divisors have integral harmonic mean up to 300, Math. Comput. 73 (2004), 475-491.

EXAMPLE

A001599(4) = 140, but 336 = sigma(140) <> 2*140 = 280. Thus, 140 is a harmonic number which is not perfect. - Muniru A Asiru, Nov 26 2018

MATHEMATICA

Select[Range[2 10^7], IntegerQ[HarmonicMean[Divisors[#]]] && !DivisorSigma[1, #]==2 # &] (* Vincenzo Librandi, Nov 27 2018 *)

PROG

(GAP) Concatenation([1], Filtered([2, 4..2000000], n->Sigma(n)<>2*n and IsInt(n*Tau(n)/Sigma(n)))); # Muniru A Asiru, Nov 26 2018

(PARI) isok(n) = my(sn = sigma(n)); (frac(n*numdiv(n)/sn) == 0) && (sn != 2*n); \\ Michel Marcus, Nov 28 2018

CROSSREFS

Cf. A001599, A003601. Different from A007340.

For the associated harmonic means, see A102408.

Sequence in context: A131492 A276026 A259718 * A140798 A249554 A196447

Adjacent sequences:  A090942 A090943 A090944 * A090946 A090947 A090948

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 28 2004

STATUS

approved

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Last modified January 18 20:57 EST 2019. Contains 319282 sequences. (Running on oeis4.)