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A324560
Numbers > 1 where the minimum prime index is less than or equal to the number of prime factors counted with multiplicity.
13
2, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 66, 68, 69, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 87, 88, 90, 92, 93, 94, 96, 98, 99, 100
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 a certain type of integer partitions counted by A039900 (but not the type of partitions described in the name). The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
FORMULA
A055396(a(n)) <= A001222(a(n)).
EXAMPLE
The sequence of terms together with their prime indices begins:
2: {1}
4: {1,1}
6: {1,2}
8: {1,1,1}
9: {2,2}
10: {1,3}
12: {1,1,2}
14: {1,4}
15: {2,3}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
21: {2,4}
22: {1,5}
24: {1,1,1,2}
26: {1,6}
27: {2,2,2}
28: {1,1,4}
30: {1,2,3}
32: {1,1,1,1,1}
MAPLE
with(numtheory):
q:= n-> is(pi(min(factorset(n)))<=bigomega(n)):
select(q, [$2..100])[]; # Alois P. Heinz, Mar 07 2019
MATHEMATICA
Select[Range[2, 100], PrimePi[FactorInteger[#][[1, 1]]]<=PrimeOmega[#]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 06 2019
STATUS
approved