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A324517
Numbers > 1 where the maximum prime index equals the number of prime factors minus the number of distinct prime factors.
19
4, 24, 27, 36, 54, 80, 200, 224, 240, 360, 405, 500, 540, 600, 625, 672, 675, 704, 784, 810, 900, 1008, 1120, 1125, 1250, 1350, 1500, 1512, 1664, 1701, 1875, 2112, 2250, 2268, 2352, 2744, 2800, 3168, 3360, 3402, 3520, 3528, 3750, 3872, 3920, 3969, 4352, 4752
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 A324518. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
FORMULA
A061395(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}
24: {1,1,1,2}
27: {2,2,2}
36: {1,1,2,2}
54: {1,2,2,2}
80: {1,1,1,1,3}
200: {1,1,1,3,3}
224: {1,1,1,1,1,4}
240: {1,1,1,1,2,3}
360: {1,1,1,2,2,3}
405: {2,2,2,2,3}
500: {1,1,3,3,3}
540: {1,1,2,2,2,3}
600: {1,1,1,2,3,3}
625: {3,3,3,3}
672: {1,1,1,1,1,2,4}
675: {2,2,2,3,3}
704: {1,1,1,1,1,1,5}
784: {1,1,1,1,4,4}
810: {1,2,2,2,2,3}
900: {1,1,2,2,3,3}
MATHEMATICA
Select[Range[2, 1000], With[{f=FactorInteger[#]}, PrimePi[f[[-1, 1]]]==Total[Last/@f]-Length[f]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 06 2019
STATUS
approved