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A360527 Numbers k such that A360522(k) = A360522(k+1).

%I A360527 #12 Jun 10 2023 07:32:52
%S A360527 4,8,14,176,895,956,957,1334,1634,1724,1725,1844,1934,2685,2871,3404,
%T A360527 3759,4047,4136,5175,7004,7315,7599,8055,12104,13760,18415,20145,
%U A360527 29392,32944,33998,42818,44095,44516,49599,60356,74918,79826,79833,84134,85172,85744,86343
%N A360527 Numbers k such that A360522(k) = A360522(k+1).
%C A360527 Numbers k such that A360522(k) = A360522(k+1) = A360522(k+2) exist: 956 and 1724. Are there any other terms like these? There are none below 1.8*10^10.
%H A360527 Amiram Eldar, <a href="/A360527/b360527.txt">Table of n, a(n) for n = 1..2500</a>
%e A360527 4 is a term since A360522(4) = A360522(5) = 6.
%t A360527 f[p_, e_] := p^e + e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Position[Partition[Array[s, 10^5], 2, 1], _?(SameQ @@ # &)] // Flatten
%o A360527 (PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^f[i,2] + f[i,2]);}
%o A360527 lista(nmax) = {my(s1 = s(1), s2); for(n=2, nmax, s2=s(n); if(s1 == s2, print1(n-1, ", ")); s1 = s2); }
%Y A360527 Cf. A360522.
%Y A360527 Similar sequences: A002961, A064115, A064125, A293183, A306985.
%K A360527 nonn
%O A360527 1,1
%A A360527 _Amiram Eldar_, Feb 10 2023