A388000 Numbers k such that phi(k) = pi(k) + tau(k).

1, 7, 21, 44, 56, 80, 156, 252, 300, 360

Offset

1,2

Comments

a(11), if it exists, is greater than 10^9. - Lyle Blosser, Jan 18 2026

Links

Table of n, a(n) for n=1..10.

Example

80 is in the sequence since phi(80) = 32 = 22 + 10 = pi(80) + tau(80).

Mathematica

Select[Range[400], EulerPhi[#] == PrimePi[#] + DivisorSigma[0, #] &] (* Amiram Eldar, Oct 14 2025 *)

Prog

(Python)
from math import prod
from itertools import count, islice
from sympy import factorint, nextprime
def agen(): # generator of terms
    pk, pik = 2, 0
    for k in count(1):
        if k == pk:
            pk, pik = nextprime(pk), pik + 1
        f = factorint(k)
        phik = prod((p - 1)*p**(e-1) for p, e in f.items())
        tauk = prod(e+1 for e in f.values())
        if phik == pik + tauk:
            yield k
print(list(islice(agen(), 10))) # Michael S. Branicky, Jan 19 2026

Crossrefs

Cf. A000005, A000010, A000720.

Sequence in context: A246430 A387625 A256051 * A299254 A146411 A287431

Adjacent sequences: A387997 A387998 A387999 * A388001 A388002 A388003

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Oct 14 2025

Status

approved