A153801 -id:A153801 - cp's OEIS frontend

A153804 a(n) = A153801(n)/2.

0, 0, 0, 0, 1, 2, 1, 6, 19, 30, 38, 45, 240, 282, 616, 1075, 1111, 1578, 2093, 2176, 4808, 4931, 5565, 9924, 10802, 11554, 22197, 43068, 55197, 65968, 107982, 378354, 429648, 628824, 699060, 1488035, 1510610, 3486215, 6733375, 10497919, 12018202, 12982385, 15201133

Offset: 1

Omar E. Pol, Jan 13 2009

nonn

Amiram Eldar, Table of n, a(n) for n = 1..48

Cf. A000040, A000043, A153800, A153801, A153802.

With[{max = 48}, (MersennePrimeExponent[Range[max]] - Prime[Range[max]]) / 2] (* Amiram Eldar, Oct 21 2024 *)

a(n) = (A000043(n) - A000040(n))/2.

More terms from R. J. Mathar, Mar 14 2009

More terms from Jinyuan Wang, Mar 02 2020

A153802 a(n) = A153800(n) - A000040(n).

Original entry on oeis.org

0, 0, 0, 0, 2, 6, 8, 22, 87, 163, 198, 257

Offset: 1

Omar E. Pol, Jan 13 2009

Cf. A000040, A000043, A000668, A000225, A000396, A007691, A153800, A153801, A153803.

a(11)-a(12) from Jinyuan Wang, Mar 01 2020

A153803 a(n) = A153800(n) - A000043(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 6, 10, 49, 103, 122, 167

Offset: 1

Omar E. Pol, Jan 13 2009

Cf. A000040, A000043, A000668, A000225, A000396, A007691, A153800, A153801, A153802.

a007691[m_] := Block[{f = 0, i = 1}, While[f < m, If[Divisible[DivisorSigma[1, i], i], ++f]; ++i;]; Return[i - 1]]
a153800[n_] := Block[{i = 2, j, f = 0}, While[f < n, j = a007691[i]; If[PerfectNumberQ[j], ++f;]; ++i]; Return[i - 1]]
a[n_] := a153800[n] - MersennePrimeExponent[n]
a /@ Range[1, 4] (* Julien Kluge, Dec 15 2016 *)

cp's OEIS Frontend

A153804 a(n) = A153801(n)/2.

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A153802 a(n) = A153800(n) - A000040(n).

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Extensions

A153803 a(n) = A153800(n) - A000043(n).

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Mathematica