Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Mar 05 2020 03:40:01
%S 3,24,360,5016,28440,42066,50568,60456,187176,998670,1454706,12055512,
%T 14365608,25726728,27896424,51670374,91702962,141084774,236280786,
%U 249854952,386668344,439362504,792554574,1115866152,1931976696,2467823442,2496238590,2655297558,2715505440
%N Solutions k of the equation isigma(k) = isigma(k-1) + isigma(k-2) where isigma(k) is the sum of the infinitary divisors of k (A049417).
%H Amiram Eldar, <a href="/A332975/b332975.txt">Table of n, a(n) for n = 1..38</a>
%e 24 is a term since isigma(24) = 60 and isigma(22) + isigma(23) = 36 + 24 = 60.
%t fun[p_, e_] := Module[{b = IntegerDigits[e, 2]}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ fun @@@ FactorInteger[n]; Select[Range[3, 10^5], isigma[#] == isigma[# - 1] + isigma[# - 2] &]
%Y The infinitary version of A065900.
%Y Cf. A049417, A065557, A075565, A076136, A076251, A145469, A291126, A291176, A292033, A294995, A332976.
%K nonn
%O 1,1
%A _Amiram Eldar_, Mar 04 2020