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A338468
Odd squarefree numbers whose prime indices have no common divisor > 1.
3
15, 33, 35, 51, 55, 69, 77, 85, 93, 95, 105, 119, 123, 141, 143, 145, 155, 161, 165, 177, 187, 195, 201, 205, 209, 215, 217, 219, 221, 231, 249, 253, 255, 265, 285, 287, 291, 295, 309, 323, 327, 329, 335, 341, 345, 355, 357, 381, 385, 391, 395, 403, 407, 411
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 relatively prime strict integer partitions with no 1's (A337452). The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions.
EXAMPLE
The sequence of terms together with their prime indices begins:
15: {2,3} 145: {3,10} 249: {2,23} 355: {3,20}
33: {2,5} 155: {3,11} 253: {5,9} 357: {2,4,7}
35: {3,4} 161: {4,9} 255: {2,3,7} 381: {2,31}
51: {2,7} 165: {2,3,5} 265: {3,16} 385: {3,4,5}
55: {3,5} 177: {2,17} 285: {2,3,8} 391: {7,9}
69: {2,9} 187: {5,7} 287: {4,13} 395: {3,22}
77: {4,5} 195: {2,3,6} 291: {2,25} 403: {6,11}
85: {3,7} 201: {2,19} 295: {3,17} 407: {5,12}
93: {2,11} 205: {3,13} 309: {2,27} 411: {2,33}
95: {3,8} 209: {5,8} 323: {7,8} 413: {4,17}
105: {2,3,4} 215: {3,14} 327: {2,29} 415: {3,23}
119: {4,7} 217: {4,11} 329: {4,15} 429: {2,5,6}
123: {2,13} 219: {2,21} 335: {3,19} 435: {2,3,10}
141: {2,15} 221: {6,7} 341: {5,11} 437: {8,9}
143: {5,6} 231: {2,4,5} 345: {2,3,9} 447: {2,35}
MATHEMATICA
Select[Range[1, 100, 2], SquareFreeQ[#]&&GCD@@PrimePi/@First/@FactorInteger[#]==1&]
CROSSREFS
A302568 is the prime or pairwise coprime version, counted by A007359.
A302697 is not required to be squarefree, counted by A302698 (ordered version: A337450).
A302796 allows evens, counted by A078374 (ordered version: A332004).
A337452 counts partitions with these Heinz numbers (ordered version: A337451).
A337984 is the pairwise coprime version, counted by A337485 (ordered version: A337697).
A005117 lists squarefree numbers.
A005408 lists odd numbers.
A056911 lists odd squarefree numbers.
A289509 lists Heinz numbers of relatively prime partitions, counted by A000837 (ordered version: A000740).
Sequence in context: A089966 A327784 A339562 * A337984 A050384 A142862
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 29 2020
STATUS
approved