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%I #12 Apr 20 2023 13:21:13
%S 24,27,48,79,120,168,199,288,350,360,378,391,447,507,528,775,840,895,
%T 960,1088,1136,1368,1638,1639,1680,1848,1849,2095,2127,2208,2322,2749,
%U 2808,3720,3726,3798,3799,3919,4050,4087,4488,4550,4872,5040,5328,5448,5631,6240
%N Numbers k such that k and k+1 are both in A362401.
%H Amiram Eldar, <a href="/A362404/b362404.txt">Table of n, a(n) for n = 1..3557</a> (terms below 10^8)
%e 24 is a term since 24 and 25 are both in the range of A162296: A162296(20) = 24 and A162296(25) = 25.
%t s[n_] := Module[{f = FactorInteger[n], p, e}, p = f[[;; , 1]]; e = f[[;; , 2]]; Times @@ ((p^(e + 1) - 1)/(p - 1)) - Times @@ (p + 1)]; s[1] = 0; seq[max_] := Module[{v = Select[Union[Array[s, max]], 0 < # <= max &], i}, i = Position[Differences[v], 1] // Flatten; v[[i]]]; seq[10^4]
%o (PARI) s(n) = {my(f = factor(n), p, e); prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; ((p^(e + 1) - 1)/(p - 1))) - prod(i = 1, #f~, f[i, 1] + 1);}
%o lista(kmax) = {my(v = select(x -> (x < kmax), Set(vector(kmax, k, s(k))))); for(k=1, #v-1, if(v[k+1] - v[k] == 1, print1(v[k], ", ")));}
%Y Subsequence of A362401.
%Y A362405 is a subsequence.
%Y Cf. A162296.
%K nonn
%O 1,1
%A _Amiram Eldar_, Apr 18 2023
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