A373532 - OEIS

%I #12 Jun 10 2024 15:00:22

%S 1,2,12,120,240,3276,2520,10920,21840,32760,65520,622440,600600,

%T 900900,3636360,1801800,3603600,4455360,22407840,8910720,17821440,

%U 51351300,46060560,69090840,92121120,126977760,138181680,380933280,245044800,414545040,490089600,507911040

%N a(n) is the least number k such that A373531(k) = n, or -1 if no such k exists.

%F a(n) >= A061799(n).

%t f[n_] := Max[Tally[EulerPhi[Divisors[n]]][[;; , 2]]]; seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = f[n]; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[12, 10^6]

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

%o lista(nmax, kmax = oo) = {my(v = vector(nmax), k = 1, c = 0, i); while(c < nmax && k < kmax, i = f(k); if(i <= nmax && v[i] == 0, c++; v[i] = k); k++); v}

%o (Python)

%o from collections import Counter

%o from itertools import count, islice

%o from sympy import divisors, totient

%o def agen(): # generator of terms

%o     adict, n = dict(), 1

%o     for k in count(1):

%o         divs = divisors(k)

%o         if len(divs) < n:

%o             continue

%o         c = Counter(totient(d) for d in divs)

%o         v = c.most_common(1)[0][1]

%o         if v not in adict:

%o             adict[v] = k

%o             while n in adict:

%o                 yield adict[n]

%o                 n += 1

%o print(list(islice(agen(), 11))) # _Michael S. Branicky_, Jun 08 2024

%Y Cf. A061799, A328857, A373531.

%K nonn

%O 1,2

%A _Amiram Eldar_, Jun 08 2024