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A unitary phi reciprocal amicable number: consider two different numbers a, b which satisfy the following equation for some integer k: uphi(a)=uphi(b)=1/k*a*b/(a-b); or equivalently, 1/uphi(a)=1/uphi(b)=k*(-1/a+1/b); sequence gives b numbers.
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%I #4 Apr 19 2016 01:07:33

%S 1,3,12,20,220,144,240,5060,5520,5520,10800,11520,8928,15120,31680,

%T 33984,56576,60372,39168,65280,80640,149760,149760,169920,281600,

%U 398200,664092,669600,940896,1235520

%N A unitary phi reciprocal amicable number: consider two different numbers a, b which satisfy the following equation for some integer k: uphi(a)=uphi(b)=1/k*a*b/(a-b); or equivalently, 1/uphi(a)=1/uphi(b)=k*(-1/a+1/b); sequence gives b numbers.

%C Here uphi(n)=A047994(n) is the unitary totient function: if n = Product p_i^e_i, uphi(n) = Product (p_i^e_i - 1).

%Y Cf. A047994, A080766, A080768, A067739, A067741.

%K nonn

%O 0,2

%A _Yasutoshi Kohmoto_

%E Kohmoto found 2nd, 6th, 13th, 25th terms. _Dean Hickerson_ calculated the other terms.