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%I #12 Jul 21 2021 00:43:00
%S 14,27,44,459,620,957,1334,1634,1652,2204,2685,3195,3451,3956,4064,
%T 4544,5547,8495,8636,8907,9844,11515,15296,19491,20145,20155,27643,
%U 31724,33998,38180,41265,41547,42818,45716,48364,61964,64665,74875,74918,79316,79826
%N Numbers k such that isigma(k) = isigma(k+1), where isigma(k) is the sum of the infinitary divisors of k (A049417).
%C a(n) differs from A293183(n) starting at n = 15.
%H Amiram Eldar, <a href="/A306985/b306985.txt">Table of n, a(n) for n = 1..1000</a>
%e 14 is in the sequence since isigma(14) = isigma(15) = 24.
%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]; aQ[n_] := isigma[n] == isigma[n+1]; Select[Range[1000], aQ]
%Y Cf. A002961, A049417, A064125, A293183.
%K nonn
%O 1,1
%A _Amiram Eldar_, Mar 18 2019
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