login
A324519
Numbers > 1 where the minimum prime index equals the number of prime factors minus the number of distinct prime factors.
15
4, 12, 18, 20, 27, 28, 44, 50, 52, 60, 68, 76, 84, 90, 92, 98, 116, 124, 126, 132, 135, 140, 148, 150, 156, 164, 172, 188, 189, 198, 204, 212, 220, 225, 228, 234, 236, 242, 244, 260, 268, 276, 284, 292, 294, 297, 306, 308, 316, 332, 338, 340, 342, 348, 350
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.
Also Heinz numbers of the integer partitions enumerated by A324520. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
LINKS
FORMULA
A055396(a(n)) = A001222(a(n)) - A001221(a(n)) = A046660(a(n)).
EXAMPLE
The sequence of terms together with their prime indices begins:
4: {1,1}
12: {1,1,2}
18: {1,2,2}
20: {1,1,3}
27: {2,2,2}
28: {1,1,4}
44: {1,1,5}
50: {1,3,3}
52: {1,1,6}
60: {1,1,2,3}
68: {1,1,7}
76: {1,1,8}
84: {1,1,2,4}
90: {1,2,2,3}
92: {1,1,9}
98: {1,4,4}
MATHEMATICA
Select[Range[2, 100], With[{f=FactorInteger[#]}, PrimePi[f[[1, 1]]]==Total[Last/@f]-Length[f]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 06 2019
STATUS
approved