A349064 Numbers k such that A183097(k) > 2*k.

144, 216, 288, 432, 576, 648, 864, 1152, 1296, 1600, 1728, 1944, 2000, 2304, 2592, 3200, 3456, 3600, 3888, 4000, 4608, 5000, 5184, 5400, 5488, 5832, 6272, 6400, 6912, 7056, 7200, 7776, 8000, 9000, 9216, 10000, 10368, 10584, 10800, 10976, 11664, 12544, 12800, 13500

Offset

1,1

Comments

The least odd term is a(934) = A349065(1) = 3472875.

Not all the terms are powerful. E.g., (prime(44)#)^3/4 and (prime(22)#)^6/32 are nonpowerful terms. What is the least nonpowerful term?

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

144 is a term since A183097(144) = 290 > 2*144 = 288.

Mathematica

f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - p; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; q[n_] := s[n] > 2*n; Select[Range[15000], q]

Prog

(PARI) isok(k) = sumdiv(k, d, ispowerful(d)*d) > 2*k; \\ Michel Marcus, Nov 07 2021

Crossrefs

Subsequence of A005101.

A349065 is a subsequence.

Cf. A001694, A183097.

Sequence in context: A135780 A069701 A358666 * A124144 A276564 A061040

Adjacent sequences: A349061 A349062 A349063 * A349065 A349066 A349067

Keyword

nonn

Author

Amiram Eldar, Nov 07 2021

Status

approved