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A372694 Numbers k such that A372692(k) = A372692(k+1) = A372692(k+2) > 1.

%I A372694 #7 May 10 2024 11:13:22
%S A372694 17784450,28873348,38990474,44534923,48780675,85648274,95438475,
%T A372694 100982924,111100050,157757850,184508323,188754075,225621674,
%U A372694 240956324,251073450,308820148,318937274,334271924,365595074,371139523,378806848,391046850,437704650,505568474,511112923
%N A372694 Numbers k such that A372692(k) = A372692(k+1) = A372692(k+2) > 1.
%C A372694 Can 4 consecutive integers have the same value of A372692? There are none below 2*10^10.
%H A372694 Amiram Eldar, <a href="/A372694/b372694.txt">Table of n, a(n) for n = 1..1200</a>
%t A372694 f[p_, e_] := p^(2^(-1 + Position[Reverse@ IntegerDigits[e, 2], _?(# == 0 &)])); s[1] = 1; s[n_] := s[n] = Times @@ (Flatten@ (f @@@ FactorInteger[n]) + 1);
%t A372694 Select[Range[10^8], (s1 = s[#]) > 1 && s1 == s[# + 1] == s[# + 2] &]
%o A372694 (PARI) s(n) = {my(f = factor(n), k); prod(i = 1, #f~, k = apply(x -> 1 - x, binary(f[i, 2])); prod(j = 1, #k, if(k[j], f[i, 1]^(2^(#k-j)) + 1, 1)));}
%o A372694 lista(kmax) = {my(s1 = s(1), s2 = s(2), s3); for(k = 3, kmax, s3 = s(k); if(s1 > 1 && s1 == s2 && s2 == s3, print1(k - 2, ", ")); s1 = s2; s2 = s3);}
%Y A372694 Subsequence of A070258 and A372693.
%Y A372694 Cf. A334021, A324310, A372692.
%K A372694 nonn
%O A372694 1,1
%A A372694 _Amiram Eldar_, May 10 2024