|
|
A363951
|
|
Numbers whose prime indices satisfy (length) = (mean), or (sum) = (length)^2.
|
|
8
|
|
|
2, 9, 10, 68, 78, 98, 99, 105, 110, 125, 328, 444, 558, 620, 783, 812, 870, 966, 988, 1012, 1035, 1150, 1156, 1168, 1197, 1254, 1326, 1330, 1425, 1521, 1666, 1683, 1690, 1704, 1785, 1870, 1911, 2002, 2125, 2145, 2275, 2401, 2412, 2541, 2662, 2680, 2695, 3025
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
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.
|
|
LINKS
|
|
|
EXAMPLE
|
The terms together with their prime indices begin:
2: {1}
9: {2,2}
10: {1,3}
68: {1,1,7}
78: {1,2,6}
98: {1,4,4}
99: {2,2,5}
105: {2,3,4}
110: {1,3,5}
125: {3,3,3}
328: {1,1,1,13}
444: {1,1,2,12}
558: {1,2,2,11}
620: {1,1,3,11}
783: {2,2,2,10}
812: {1,1,4,10}
870: {1,2,3,10}
966: {1,2,4,9}
988: {1,1,6,8}
|
|
MATHEMATICA
|
prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Mean[prix[#]]==PrimeOmega[#]&]
|
|
CROSSREFS
|
Partitions of this type are counted by A364055, without zeros A206240.
A363950 ranks partitions with low mean 2, counted by A026905 redoubled.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|