cp's OEIS Frontend

A326621 Numbers n such that the average of the set of distinct prime indices of n is an integer.

%I A326621 #4 Jul 15 2019 01:44:40
%S A326621 2,3,4,5,7,8,9,10,11,13,16,17,19,20,21,22,23,25,27,29,30,31,32,34,37,
%T A326621 39,40,41,43,44,46,47,49,50,53,55,57,59,60,61,62,63,64,67,68,71,73,78,
%U A326621 79,80,81,82,83,85,87,88,89,90,91,92,94,97,100,101,103,105
%N A326621 Numbers n such that the average of the set of distinct prime indices of n is an integer.
%C A326621 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A326621 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions whose distinct parts have an integer average.
%e A326621 The sequence of terms together with their prime indices begins:
%e A326621     2: {1}
%e A326621     3: {2}
%e A326621     4: {1,1}
%e A326621     5: {3}
%e A326621     7: {4}
%e A326621     8: {1,1,1}
%e A326621     9: {2,2}
%e A326621    10: {1,3}
%e A326621    11: {5}
%e A326621    13: {6}
%e A326621    16: {1,1,1,1}
%e A326621    17: {7}
%e A326621    19: {8}
%e A326621    20: {1,1,3}
%e A326621    21: {2,4}
%e A326621    22: {1,5}
%e A326621    23: {9}
%e A326621    25: {3,3}
%e A326621    27: {2,2,2}
%e A326621    29: {10}
%t A326621 Select[Range[2,100],IntegerQ[Mean[PrimePi/@First/@FactorInteger[#]]]&]
%Y A326621 Positions of 1's in A326620.
%Y A326621 Cf. A051293, A056239, A067538, A078174, A078175, A102627, A112798, A326567/A326568, A326619/A326620, A326622.
%K A326621 nonn
%O A326621 1,1
%A A326621 _Gus Wiseman_, Jul 14 2019