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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 (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.
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).
LINKS
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[#]&]
CROSSREFS
Sequence in context: A338924 A065090 A371167 * A355822 A367226 A227197
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 06 2019
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)