A389855 Numbers k such that sigma(k) = psi(k) + tau(k) + pi(k).

56, 188, 11817, 12051, 16461, 24561, 474150, 2742950, 50306150, 50307350, 401027475, 566757125

Offset

1,1

Comments

From Aloe Poliszuk, Oct 23 2025: (Start)

a(n) is never squarefree.

Also, numbers k such that Sum_{d|k} (k/d * A107078(d) - 1) = pi(k). (End)

Links

Table of n, a(n) for n=1..12.

Example

56 is in the sequence since sigma(56) = 120 = 96 + 8 + 16 = psi(56) + tau(56) + pi(56).

Prog

(PARI) dedpsi(f) = prod(k = 1, #f~, (f[k, 1]+1) * f[k, 1]^(f[k, 2]-1));
list(lim) = {my(q = 2, m = 0, f); forprime(p = 3, lim, m++; for(k = q, p-1, f = factor(k); if(sigma(f) == dedpsi(f) + numdiv(f) + m, print1(k, ", "))); q = p); } \\ Amiram Eldar, Oct 17 2025

Crossrefs

Cf. A000005, A000203, A000720, A001615, A387953, A387999, A388001, A389856.

Cf. A013929, A107078.

Sequence in context: A234114 A392951 A234107 * A136547 A264303 A200833

Adjacent sequences: A389852 A389853 A389854 * A389856 A389857 A389858

Keyword

nonn,hard,more

Author

S. I. Dimitrov, Oct 17 2025

Extensions

a(7)-a(12) from Amiram Eldar, Oct 17 2025

Status

approved