A327774 Composite numbers m such that tau_k(m) = m for some k, where tau_k is the k-th Piltz divisor function (A077592).

18, 36, 75, 100, 200, 224, 225, 441, 560, 1183, 1344, 1920, 3025, 8281, 26011, 34606, 64009, 72030, 76895, 115351, 197173, 280041, 494209, 538265, 1168561, 1947271, 2927521, 3575881, 3613153, 3780295, 4492125, 7295401, 10665331, 11580409, 12511291, 13476375, 15381133

Offset

1,1

Comments

The prime numbers are excluded from this sequence since tau_p(p) = p for all primes p.

The corresponding values of k are 3, 3, 5, 4, 4, 4, 5, 6, 4, 13, 4, 4, 10, 13, 37, 11, 22, 7, 13, 61, 73, 17, 37, 13, 46, 157, 58, 61, 193, 29, 9, 73, 277, 82, 37, 9, 313, ...

Links

Table of n, a(n) for n=1..37.

Example

18 is in the sequence since tau_3(18) = A007425(18) = 18.

Mathematica

fun[e_, k_] := Times @@ (Binomial[# + k - 1, k - 1] & /@ e); tau[n_, k_] := fun[ FactorInteger[n][[;; , 2]], k]; aQ[n_] := CompositeQ[n] && Module[{k = 2}, While[(t = tau[n, k]) < n, k++]; t == n]; Select[Range[10^5], aQ]

Crossrefs

Cf. A097989.

Cf. A007425, A007426, A034695, A061200, A077592, A111217, A111218, A111219, A111220, A111221, A111306, A163272.

Sequence in context: A156903 A204824 A252424 * A335784 A347889 A375679

Adjacent sequences: A327771 A327772 A327773 * A327775 A327776 A327777

Keyword

nonn

Author

Amiram Eldar, Sep 25 2019

Status

approved