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
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).
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 29 2020
STATUS
approved