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Positions of superabundant numbers in the sequence of primorial products.
6

%I #24 Nov 06 2023 01:12:27

%S 1,2,3,4,6,8,11,12,13,17,20,24,27,34,36,43,47,55,67,84,95,107,112,138,

%T 166,183,211,220,252,261,264,314,348,390,406,457,476,500,582,652,726,

%U 756,839,870,907,1046,1188,1199,1294,1310,1359,1500,1553,1615,1835

%N Positions of superabundant numbers in the sequence of primorial products.

%C Indices of A004394 in A025487; the latter is easily seen to contain the former.

%H Michael De Vlieger, <a href="/A293635/b293635.txt">Table of n, a(n) for n = 1..300</a> (first 84 terms from Robert Price)

%t Block[{P = Product[Prime@ i, {i, 7}], s, t, u}, s = Array[DivisorSigma[1, #]/# &, P]; t = Array[If[# == 1, {0}, Sort[FactorInteger[#][[All, -1]], Greater]] &, P]; u = Values[PositionIndex@ t][[All, 1]]; Map[FirstPosition[u, #][[1]] &, FirstPosition[s, #][[1]] & /@ Union@ FoldList[Max, s]]] (* _Michael De Vlieger_, Oct 14 2017 *)

%Y Cf. A002110, A004394, A025487.

%K nonn

%O 1,2

%A _Allan C. Wechsler_, Oct 13 2017

%E More terms from _Michael De Vlieger_, Oct 14 2017

%E More terms from _Robert Price_, Oct 19 2017