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A373531 a(n) is the maximum number of divisors of n with an equal value of the Euler totient function (A000010).

%I A373531 #18 Jun 10 2024 15:00:31
%S A373531 1,2,1,2,1,2,1,2,1,2,1,3,1,2,1,2,1,2,1,2,1,2,1,3,1,2,1,2,1,2,1,2,1,2,
%T A373531 1,3,1,2,1,3,1,2,1,2,1,2,1,3,1,2,1,2,1,2,1,2,1,2,1,3,1,2,2,2,1,2,1,2,
%U A373531 1,2,1,3,1,2,1,2,1,2,1,3,1,2,1,3,1,2,1
%N A373531 a(n) is the maximum number of divisors of n with an equal value of the Euler totient function (A000010).
%C A373531 The sums of the first 10^k terms, for k = 1, 2, ..., are 15, 161, 1641, 16554, 166029, 1662306, 16630535, 166335597, 1663473941, 16635216306, ... . Apparently, this sequence has an asymptotic mean 1.663... .
%H A373531 Amiram Eldar, <a href="/A373531/b373531.txt">Table of n, a(n) for n = 1..10000</a>
%F A373531 a(A326835(n)) = 1.
%F A373531 a(A359563(n)) >= 2.
%F A373531 a(A359565(n)) >= 3.
%F A373531 a(2*n) >= 2.
%F A373531 a(p) = 2 for an odd prime p.
%F A373531 a(m*n) >= a(n) for all m > 1.
%e A373531 a(2) = 2 since 2 has 2 divisors, 1 and 2, and phi(1) = phi(2) = 1.
%e A373531 a(12) = 3 since 3 of the divisors of 12 (3, 4 and 6) have the same value of phi: phi(3) = phi(4) = phi(6) = 2.
%t A373531 a[n_] := Max[Tally[EulerPhi[Divisors[n]]][[;; , 2]]]; Array[a, 100]
%o A373531 (PARI) a(n) = vecmax(matreduce(apply(x->eulerphi(x), divisors(n)))[ , 2]);
%o A373531 (Python)
%o A373531 from collections import Counter
%o A373531 from sympy import divisors, totient
%o A373531 def a(n):
%o A373531     c = Counter(totient(d) for d in divisors(n, generator=True))
%o A373531     return c.most_common(1)[0][1]
%o A373531 print([a(n) for n in range(1, 88)]) # _Michael S. Branicky_, Jun 08 2024
%Y A373531 Cf. A000010, A102190, A319696, A326835, A359563, A359565, A373532.
%K A373531 nonn,easy
%O A373531 1,2
%A A373531 _Amiram Eldar_, Jun 08 2024