A379030 Nonsquarefree modified exponential abundant numbers: nonsquarefree numbers k such that A241405(k) > 2*k.

120, 150, 168, 270, 294, 420, 630, 660, 726, 750, 780, 840, 924, 990, 1014, 1020, 1050, 1092, 1140, 1170, 1320, 1380, 1386, 1428, 1470, 1530, 1560, 1596, 1638, 1650, 1710, 1734, 1740, 1848, 1860, 1890, 1950, 2040, 2058, 2070, 2142, 2166, 2184, 2220, 2280, 2394

Offset

1,1

Comments

All the squarefree abundant numbers (A087248) are also modified exponential abundant numbers (A379029). This sequence lists the terms of A379029 that are not in A087248.

The numbers of terms that do no exceed 10^k, for k = 3, 4, ..., are 14, 211, 2090, 21236, 212744, 2123071, 21235175, 212450318, ... . Apparently, the asymptotic density of this sequence exists and equals 0.0212... .

Links

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

Mathematica

f[p_, e_] := DivisorSum[e + 1, p^(# - 1) &]; mesigma[1] = 1; mesigma[n_] := Times @@ f @@@ FactorInteger[n]; nsmeAbQ[n_] := !SquareFreeQ[n] && mesigma[n] > 2*n; Select[Range[2400], nsmeAbQ]

Prog

(PARI) is(n) = {my(f=factor(n)); if(issquarefree(f), 0, prod(i=1, #f~, sumdiv(f[i, 2]+1, d, f[i, 1]^(d-1))) > 2*n); }

Crossrefs

Intersection of A013929 and A379029.

Complement of A087248 within A379029.

Cf. A005117, A241405.

Sequence in context: A248662 A259826 A192277 * A034291 A039602 A316835

Adjacent sequences: A379027 A379028 A379029 * A379031 A379032 A379033

Keyword

nonn,easy

Author

Amiram Eldar, Dec 14 2024

Status

approved