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 integer partitions with no 1's whose distinct parts are pairwise coprime (A338315). 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} 135: {2,2,2,3} 215: {3,14}
33: {2,5} 141: {2,15} 217: {4,11}
35: {3,4} 143: {5,6} 219: {2,21}
45: {2,2,3} 145: {3,10} 221: {6,7}
51: {2,7} 153: {2,2,7} 225: {2,2,3,3}
55: {3,5} 155: {3,11} 245: {3,4,4}
69: {2,9} 161: {4,9} 249: {2,23}
75: {2,3,3} 165: {2,3,5} 253: {5,9}
77: {4,5} 175: {3,3,4} 255: {2,3,7}
85: {3,7} 177: {2,17} 265: {3,16}
93: {2,11} 187: {5,7} 275: {3,3,5}
95: {3,8} 201: {2,19} 279: {2,2,11}
99: {2,2,5} 205: {3,13} 287: {4,13}
119: {4,7} 207: {2,2,9} 291: {2,25}
123: {2,13} 209: {5,8} 295: {3,17}
MATHEMATICA
Select[Range[1, 100, 2], CoprimeQ@@Union[PrimePi/@First/@FactorInteger[#]]&]
CROSSREFS
A337694 is a pairwise non-coprime instead of pairwise coprime version.
A337984 is the squarefree case.
A338315 counts the partitions with these Heinz numbers.
A338316 considers singletons coprime.
A007359 counts partitions into singleton or pairwise coprime parts with no 1's, with Heinz numbers A302568.
A304709 counts partitions whose distinct parts are pairwise coprime.
A337561 counts pairwise coprime strict compositions.
A337697 counts pairwise coprime compositions with no 1's.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 23 2020
STATUS
approved