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Multiply perfect numbers that are also harmonic numbers but are not arithmetic numbers.
6

%I #23 May 09 2024 03:25:58

%S 28,496,8128,2178540,33550336,142990848,459818240,1379454720,

%T 8589869056,43861478400,66433720320,137438691328,704575228896,

%U 181742883469056,6088728021160320,14942123276641920,20158185857531904,275502900594021408,622286506811515392,2305843008139952128

%N Multiply perfect numbers that are also harmonic numbers but are not arithmetic numbers.

%H Amiram Eldar, <a href="/A046986/b046986.txt">Table of n, a(n) for n = 1..207</a>

%F Let s1 be the sum of divisors of k and s0 be the number of divisors of k. Then, k is a term if k | s1, s1 | (k * s0), but s1 is not divisible by s0.

%e k = 2178540 is a term since s0 = d(k) = 216 and s1 = sigma(k) = 8714160, s1/s0 = 8714160/216 = 121030/3 is not an integer, and (k * s0)/s1 = (2178540 * 216)/8714160 = 54 and s1/k = 8714160/2178540 = 4 are integers.

%Y In A007691 and A001599 but not in A003601.

%Y Cf. A000005, A000203, A046985, A046987.

%K nonn

%O 1,1

%A _Labos Elemer_

%E a(12)-a(17) from _Donovan Johnson_, Nov 30 2008

%E Edited and a(18)-a(21) added by _Amiram Eldar_, May 09 2024