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A335198 Infinitary Zumkeller numbers (A335197) whose number of divisors is not a power of 2. 2
60, 72, 90, 96, 150, 294, 360, 420, 480, 486, 504, 540, 600, 630, 660, 672, 726, 756, 780, 792, 864, 924, 936, 960, 990, 1014, 1020, 1050, 1056, 1092, 1120, 1140, 1152, 1170, 1176, 1188, 1224, 1248, 1344, 1350, 1368, 1380, 1386, 1400, 1428, 1440, 1470, 1500, 1530 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Zumkeller numbers (A083207) whose number of divisors is a power of 2 (A036537) are also infinitary Zumkeller numbers (A335197), since all of their divisors are infinitary.

LINKS

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

EXAMPLE

72 is a term since its set of infinitary divisors, {1, 2, 4, 8, 9, 18, 36, 72}, can be partitioned into the two disjoint sets, {1, 2, 72} and {4, 8, 9, 18, 36}, whose sum is equal: 1 + 2 + 72 = 4 + 8 + 9 + 18 + 36 = 75.

MATHEMATICA

infdivs[n_] := If[n == 1, {1}, Sort @ Flatten @ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]]; infZumQ[n_] := Module[{d = infdivs[n], sum, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]]; pow2Q[n_] := n == 2^IntegerExponent[n, 2]; Select[Range[1500], ! pow2Q[DivisorSigma[0, #]] && infZumQ[#] &] (* after Michael De Vlieger at A077609 *)

CROSSREFS

Subsequence of A335197.

Cf. A083207, A036537.

Sequence in context: A030630 A068350 A265712 * A335935 A347935 A347938

Adjacent sequences:  A335195 A335196 A335197 * A335199 A335200 A335201

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 26 2020

STATUS

approved

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Last modified September 27 13:12 EDT 2022. Contains 357062 sequences. (Running on oeis4.)