The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A339981 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A339981

Primitive coreful Zumkeller numbers: coreful Zumkeller numbers (A339979) having no coreful Zumkeller aliquot divisor.
(history; published version)

#4 by Susanna Cuyler at Fri Dec 25 19:32:45 EST 2020

STATUS

proposed

approved

#3 by Amiram Eldar at Fri Dec 25 17:07:37 EST 2020

STATUS

editing

proposed

#2 by Amiram Eldar at Fri Dec 25 16:01:30 EST 2020

NAME

allocated for Amiram EldarPrimitive coreful Zumkeller numbers: coreful Zumkeller numbers (A339979) having no coreful Zumkeller aliquot divisor.

DATA

36, 200, 392, 1936, 2704, 4900, 9248, 11552, 16928, 26912, 30752, 60500, 84500, 87616, 99225, 107584, 118336, 141376, 163592, 165375, 179776, 222784, 231525, 238144, 349448, 574592, 645248, 682112, 798848, 881792, 1013888, 1204352, 1225125, 1305728, 1357952

OFFSET

1,1

COMMENTS

If m is a coreful Zumkeller number and k is a squarefree number such that gcd(m, k) = 1, then k*m is also a coreful Zumkeller number.

EXAMPLE

a(1) = 36 since it is the least coreful Zumkeller number.

The next coreful Zumkeller numbers, 72, 144 and 180, are not terms since they are multiples of 36.

MATHEMATICA

corZumQ[n_] := corZumQ[n] = Module[{r = Times @@ FactorInteger[n][[;; , 1]], d, sum, x}, d = r*Divisors[n/r]; (sum = Plus @@ d) >= 2*n && EvenQ[sum] && CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]; primczQ[n_] := corZumQ[n] && NoneTrue[Most @ Divisors[n], corZumQ]; Select[Range[10^6], primczQ]

CROSSREFS

Subsequence of A339979.

A307959 is a subsequence.

Similar sequence: A180332.

KEYWORD

allocated

nonn

AUTHOR

Amiram Eldar, Dec 25 2020

STATUS

approved

editing

#1 by Amiram Eldar at Fri Dec 25 15:51:09 EST 2020

NAME

allocated for Amiram Eldar

KEYWORD

allocated

STATUS

approved