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Solutions k of the equation usigma(k) = usigma(k-1) + usigma(k-2) where usigma(k) is the sum of unitary divisors of k (A034448).
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%I #11 Mar 10 2020 21:56:38

%S 3,42,188970,998670,51670374,91397154,236280786,259172826,792554574,

%T 1106710914,1468869930,1957827498,2467823442,2496238590,3324585210,

%U 4055970282,4183629690,4384566870,13479861630,20681058270,29343074178,43449285210,68705958690,71418085926

%N Solutions k of the equation usigma(k) = usigma(k-1) + usigma(k-2) where usigma(k) is the sum of unitary divisors of k (A034448).

%H Giovanni Resta, <a href="/A332973/b332973.txt">Table of n, a(n) for n = 1..64</a> (terms < 10^13)

%e 42 is a term since s(42) = 96 and s(40) + s(41) = 54 + 42 = 96.

%t usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); Select[Range[3, 10^8], usigma[#] == usigma[# - 1] + usigma[# - 2] &]

%o (PARI) usigma(k) = sumdivmult(k, d, if(gcd(d, k/d)==1, d)); \\ A034448

%o isok(k) = usigma(k) == usigma(k-1) + usigma(k-2); \\ _Jinyuan Wang_, Mar 08 2020

%Y The unitary version of A065900.

%Y Cf. A034448, A065557, A075565, A076136, A145469, A291126, A291176, A292033, A294995, A332974.

%K nonn

%O 1,1

%A _Amiram Eldar_, Mar 04 2020

%E Terms a(22) and beyond from _Giovanni Resta_, Mar 10 2020