A282900 -id:A282900 - cp's OEIS frontend

A327633 Noninfinitary perfect numbers: numbers k whose sum of noninfinitary divisors equals k.

112, 1344, 32512, 390144, 483840, 5930176, 2952609792

Offset: 1

Amiram Eldar, Sep 20 2019

Numbers k such that sigma(k) - isigma(k) = A000203(k) - A049417(k) = k.

No more terms below 3 * 10^10.

			112 is in the sequence since its noninfinitary divisors are {2, 4, 8, 14, 28, 56} whose sum is 112.

Cf. A000203, A007357, A049417, A064591, A077609, A282900, A282940.

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], ?(# == 1 &)])); nisigma[1] = 0; nisigma[n] := DivisorSigma[1, n] - Times @@ (Flatten @ (f @@@ FactorInteger[n]) + 1); Select[Range[500000], nisigma[#] == # &]

A282940 Largest non-infinitary divisor of A162643(n) having no non-infinitary divisors.

Original entry on oeis.org

2, 3, 6, 8, 6, 10, 5, 14, 8, 6, 22, 15, 24, 7, 10, 26, 30, 21, 8, 34, 24, 15, 38, 40, 27, 42, 30, 46, 24, 14, 33, 10, 54, 56, 58, 39, 11, 62, 42, 66, 70, 24, 21, 74, 30, 51, 78, 40, 54, 82, 13, 57, 86, 35, 88, 30, 94, 24, 14, 66, 40, 102, 69, 104, 106, 110, 56

Offset: 1

Vladimir Shevelev, Feb 25 2017

nonn

Or largest term of A036537 dividing A162643(n) (cf. our comment in A036537).

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

Cf. A000005, A036537, A162643, A282900, A327839, A372379.

f[p_, e_] := p^(2^Floor[Log2[e + 1]] - 1); s[1] = Nothing; s[n_] := Module[{v = Times @@ f @@@ FactorInteger[n]}, If[v == n, Nothing, v]]; Array[s, 300] (* Amiram Eldar, Apr 29 2024 *)

a(n) = A036537(m), where m = max{k: A036537(k)|A162643(n)}.
From Amiram Eldar, Apr 29 2024: (Start)
a(n) = A372379(A162643(n)).
Sum_{k=1..n} a(k) ~ ((c-d)/(1-d)^2) * n^2 / 2, where d = A327839 and c = 0.7907361848... is the constant in the asymptotic formula in A372379. (End)

More terms from Peter J. C. Moses, Feb 25 2017

cp's OEIS Frontend

A327633 Noninfinitary perfect numbers: numbers k whose sum of noninfinitary divisors equals k.

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