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Numbers k such that A025487(k) and A025487(k+1) have an equal number of divisors.
2

%I #10 Aug 06 2024 11:15:17

%S 4,8,15,22,69,116,122,134,135,168,208,278,400,453,538,584,718,1019,

%T 1409,1671,1799,2035,2417,2541,2595,2783,3424,3809,3860,4415,5628,

%U 6267,6672,6745,6872,6873,7277,9436,9845,10182,10191,10936,11272,11472,12105,16139,16277

%N Numbers k such that A025487(k) and A025487(k+1) have an equal number of divisors.

%C Numbers k such that A146288(k) = A146288(k+1).

%C The corresponding values of A146288(k) are 4, 8, 12, 16, 48, 48, 96, 80, 80, ... .

%C The corresponding values of A025487(k) are 6, 24, 72, 210, 5400, ... (A375196).

%C Numbers k such that A146288(k) = A146288(k+1) = A146288(k+2) are 134, 6872, 6699401, 12421946, ... .

%H Amiram Eldar, <a href="/A375195/b375195.txt">Table of n, a(n) for n = 1..4390</a>

%F A025487(a(n)) = A375196(n).

%e 4 is a term since A146288(4) = A146288(5) = 4.

%t With[{lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]}, Position[Differences[DivisorSigma[0, lps]], 0] // Flatten]

%Y Cf. A000005, A025487, A146288, A375196.

%K nonn

%O 1,1

%A _Amiram Eldar_, Aug 04 2024