

A339981


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


0



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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.


LINKS



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



KEYWORD

nonn


AUTHOR



STATUS

approved



