%I #4 Dec 25 2020 19:32:45

%S 36,200,392,1936,2704,4900,9248,11552,16928,26912,30752,60500,84500,

%T 87616,99225,107584,118336,141376,163592,165375,179776,222784,231525,

%U 238144,349448,574592,645248,682112,798848,881792,1013888,1204352,1225125,1305728,1357952

%N Primitive coreful Zumkeller numbers: coreful Zumkeller numbers (A339979) having no coreful Zumkeller aliquot divisor.

%C 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.

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

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

%t 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]

%Y Subsequence of A339979.

%Y A307959 is a subsequence.

%Y Similar sequence: A180332.

%K nonn

%O 1,1

%A _Amiram Eldar_, Dec 25 2020