A379031 Odd modified exponential abundant numbers: odd numbers k such that A241405(k) > 2*k.

15015, 19635, 21945, 23205, 25935, 26565, 31395, 33495, 33915, 35805, 39585, 41055, 42315, 42735, 45885, 47355, 49665, 50505, 51765, 54285, 55965, 58695, 61215, 64155, 68145, 70455, 72345, 77385, 80535, 82005, 83265, 84315, 91245, 95865, 102795, 112035, 116655

Offset: 1

Author

Amiram Eldar, Dec 14 2024

Keywords

• nonn
• easy

Comments

First differs from its subsequences A112643 and A249263 at n = 51: a(51) = 195195 is not a term of these two sequences.

First differs from its subsequence A129485 at n = 363: a(363) = 2537535 is not a term of A129485.

First differs from A339938 at n = 28: A339938(28) = 75075 is not a term of this sequence.

First differs from A360526 at n = 46: A360526(46) = 165165 is not a term of this sequence.

Links

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

Crossrefs

Intersection of A005408 and A379029.

Subsequence of A005231.

Subsequences: A112643, A129485, A249263.

Cf. A241405.

Similar sequences: A094889, A127666, A129485, A293186, A321147, A339938, A348275, A360526.

Programs

Mathematica

f[p_, e_] := DivisorSum[e + 1, p^(# - 1) &]; mesigma[1] = 1; mesigma[n_] := Times @@ f @@@ FactorInteger[n]; meAbQ[n_] := mesigma[n] > 2*n; Select[Range[1, 10^5, 2], meAbQ]

PARI

is(k) = if(!(k%2), 0, my(f=factor(k)); prod(i=1, #f~, sumdiv(f[i, 2]+1, d, f[i, 1]^(d-1))) > 2*k);