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%I #7 May 10 2024 11:13:12
%S 7380,18755,24804,25631,26299,27467,32799,44891,49196,49725,50940,
%T 53603,59652,64386,71027,79739,85788,89300,94275,103212,105056,105875,
%U 124992,129348,132011,138060,141899,147100,149435,155484,158147,164196,170324,175571,181620,184283
%N Numbers k such that A372692(k) = A372692(k+1) > 1.
%C The numbers k such that A372692(k) = A372692(k+1) = 1 are in A372690.
%H Amiram Eldar, <a href="/A372693/b372693.txt">Table of n, a(n) for n = 1..10000</a>
%t 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 Select[Range[10^5], (s1 = s[#]) > 1 && s1 == s[# + 1] &]
%o (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 lista(kmax) = {my(s1 = s(1), s2); for(k = 2, kmax, s2 = s(k); if(s1 > 1 && s1 == s2, print1(k - 1, ", ")); s1 = s2);}
%Y Cf. A036537, A372690, A372692.
%Y Subsequence of A068781.
%Y A372694 is a subsequence.
%Y Similar sequences: Cf. A002961, A064125, A293183, A306985, A343819, A348346.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 10 2024
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