A348274 -id:A348274 - cp's OEIS frontend

A348521 Numbers k such that A348271(k) > 2*k.

3600, 5040, 6480, 7056, 7920, 9072, 9360, 11088, 11520, 12240, 13680, 14400, 16128, 16560, 18000, 20880, 22320, 25200, 32400, 35280, 39600, 44100, 45360, 46800, 55440, 56700, 57600, 58320, 58800, 61200, 63504, 65520, 68400, 69300, 71280, 75600, 77616, 79380, 80640

Offset: 1

Amiram Eldar, Oct 21 2021

nonn

Odd terms exist (e.g., 349476304574870948475). What is the smallest odd term?

			3600 is a term since the sum of the noninfinitary divisors of 3600 is A348271(3600) = 8073 > 2*3600 = 7200.

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

Cf. A348271, A348274.

Similar sequence: A063846.

f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 1 + p^(2^(m - j)), 1], {j, 1, m}]]; isigma[1] = 1; isigma[n_] := Times @@ f @@@ FactorInteger[n]; s[n_] := DivisorSigma[1,n] - isigma[n]; Select[Range[10^5], s[#] > 2*# &]

A348527 Noninfinitary Zumkeller numbers: numbers whose set of noninfinitary divisors is nonempty and can be partitioned into two disjoint sets of equal sum.

Original entry on oeis.org

48, 80, 96, 112, 150, 180, 240, 252, 294, 336, 360, 396, 432, 468, 480, 486, 504, 528, 560, 600, 612, 624, 630, 672, 684, 720, 726, 768, 792, 810, 816, 828, 864, 880, 912, 936, 960, 1008, 1014, 1040, 1044, 1050, 1056, 1104, 1116, 1120, 1134, 1176, 1200, 1232, 1248

Offset: 1

Amiram Eldar, Oct 21 2021

nonn

The smallest odd term is a(104) = 2475.

			48 is a term since its set of noninfinitary divisors, {2, 4, 6, 8, 12, 24}, can be partitioned into the two disjoint sets, {2, 6, 8, 12} and {4, 24}, whose sums are equal: 2 + 6 + 8 + 12 = 4 + 24 = 28.

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

Cf. A348271, A348274, A348341.

Similar sequences: A083207, A290466, A335215, A335142, A335197, A335218.

nidiv[1] = {}; nidiv[n_] := Complement[Divisors[n], Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; nizQ[n_] := Module[{d = nidiv[n], sum, x}, sum = Plus @@ d; sum > 0 && EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]; Select[Range[1250], !IntegerQ@ Log2@ DivisorSigma[0, #] && nizQ[#] &]

cp's OEIS Frontend

A348521 Numbers k such that A348271(k) > 2*k.

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