A373532 a(n) is the least number k such that A373531(k) = n, or -1 if no such k exists.

1, 2, 12, 120, 240, 3276, 2520, 10920, 21840, 32760, 65520, 622440, 600600, 900900, 3636360, 1801800, 3603600, 4455360, 22407840, 8910720, 17821440, 51351300, 46060560, 69090840, 92121120, 126977760, 138181680, 380933280, 245044800, 414545040, 490089600, 507911040

Offset: 1

Author

Amiram Eldar, Jun 08 2024

Keywords

• nonn

Crossrefs

Cf. A061799, A328857, A373531.

Programs

Mathematica

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]

PARI

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

Python

from collections import Counter
from itertools import count, islice
from sympy import divisors, totient
def agen(): # generator of terms
    adict, n = dict(), 1
    for k in count(1):
        divs = divisors(k)
        if len(divs) < n:
            continue
        c = Counter(totient(d) for d in divs)
        v = c.most_common(1)[0][1]
        if v not in adict:
            adict[v] = k
            while n in adict:
                yield adict[n]
                n += 1
print(list(islice(agen(), 11))) # Michael S. Branicky, Jun 08 2024

Formula

a(n) >= A061799(n).