A373529 - OEIS

A373529

Numbers k such that k and k+1 both have at least three divisors with the same value of the Euler totient function (A000010).

%I #8 Jun 08 2024 15:44:58

%S 32319,111320,175959,179360,191919,212120,246519,254079,254960,279279,

%T 319599,355508,357399,398600,436149,463239,512000,520064,524799,

%U 542240,580040,606879,657152,678699,685880,701631,718640,726920,739556,750519,759759,775775,787815

%N Numbers k such that k and k+1 both have at least three divisors with the same value of the Euler totient function (A000010).

%C Numbers k such that k and k+1 are both in A359565.

%H Amiram Eldar, <a href="/A373529/b373529.txt">Table of n, a(n) for n = 1..10000</a>

%t q[n_] := q[n] = Max[Tally[EulerPhi[Divisors[n]]][[;; , 2]]] > 2; Select[Range[3*10^6], q[#] && q[# + 1] &]

%o (PARI) is(k) = vecmax(matreduce(apply(x->eulerphi(x), divisors(k)))[,2]) > 2;

%o lista(kmax) = {my(q1 = 0, q2); for(k = 2, kmax, q2 = is(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}

%Y Subsequence of A359565.

%Y A373530 is a subsequence.

%Y Cf. A000010, A102190.

%K nonn

%O 1,1

%A _Amiram Eldar_, Jun 08 2024