A362400 - OEIS

%I #11 Apr 20 2023 13:20:49

%S 135,819,1863,9207,10340,41124,75051,95336,278972,305091,465596,

%T 544924,570411,711027,903804,977876,1114695,1327095,1444779,1520684,

%U 1760571,1987371,2083491,2303091,2581928,2842324,2869011,3062631,3243140,4043624,4335848,4469984,4598091

%N Numbers k such that A162296(k) = A162296(k+1) > 0.

%C A162296(k) = A162296(k+1) = 0 if and only if k and k+1 are both squarefree (A005117), i.e., k is in A007674.

%H Amiram Eldar, <a href="/A362400/b362400.txt">Table of n, a(n) for n = 1..527</a> (terms below 10^10)

%e 135 is a term since A162296(135) = A162296(136) = 216.

%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)]; Select[Range[2, 5*10^6], (sn = s[#]) > 0 && sn == s[# + 1] &]

%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(s1 = s(1), s2); for(k=2, kmax, s2 = s(k); if(s1 > 0 && s2 == s1, print1(k-1, ", ")); s1 = s2); }

%Y Cf. A005117, A007674, A162296.

%Y Subsequence of A013929 and A068781.

%Y Similar sequences: A002961, A064115, A064125, A164522, A164557, A293183, A306985, A325175, A324295.

%K nonn

%O 1,1

%A _Amiram Eldar_, Apr 18 2023