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A329631
Irregular triangle read by rows where row n lists the prime indices of the n-th squarefree number.
11
1, 2, 3, 1, 2, 4, 1, 3, 5, 6, 1, 4, 2, 3, 7, 8, 2, 4, 1, 5, 9, 1, 6, 10, 1, 2, 3, 11, 2, 5, 1, 7, 3, 4, 12, 1, 8, 2, 6, 13, 1, 2, 4, 14, 1, 9, 15, 2, 7, 16, 3, 5, 2, 8, 1, 10, 17, 18, 1, 11, 3, 6, 1, 2, 5, 19, 2, 9, 1, 3, 4, 20, 21, 1, 12, 4, 5, 1, 2, 6
OFFSET
1,2
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.
EXAMPLE
Triangle begins:
1: {} 33: {2,5} 66: {1,2,5} 97: {25}
2: {1} 34: {1,7} 67: {19} 101: {26}
3: {2} 35: {3,4} 69: {2,9} 102: {1,2,7}
5: {3} 37: {12} 70: {1,3,4} 103: {27}
6: {1,2} 38: {1,8} 71: {20} 105: {2,3,4}
7: {4} 39: {2,6} 73: {21} 106: {1,16}
10: {1,3} 41: {13} 74: {1,12} 107: {28}
11: {5} 42: {1,2,4} 77: {4,5} 109: {29}
13: {6} 43: {14} 78: {1,2,6} 110: {1,3,5}
14: {1,4} 46: {1,9} 79: {22} 111: {2,12}
15: {2,3} 47: {15} 82: {1,13} 113: {30}
17: {7} 51: {2,7} 83: {23} 114: {1,2,8}
19: {8} 53: {16} 85: {3,7} 115: {3,9}
21: {2,4} 55: {3,5} 86: {1,14} 118: {1,17}
22: {1,5} 57: {2,8} 87: {2,10} 119: {4,7}
23: {9} 58: {1,10} 89: {24} 122: {1,18}
26: {1,6} 59: {17} 91: {4,6} 123: {2,13}
29: {10} 61: {18} 93: {2,11} 127: {31}
30: {1,2,3} 62: {1,11} 94: {1,15} 129: {2,14}
31: {11} 65: {3,6} 95: {3,8} 130: {1,3,6}
MATHEMATICA
Table[PrimePi/@First/@If[k==1, {}, FactorInteger[k]], {k, Select[Range[30], SquareFreeQ]}]
CROSSREFS
Row sums are A319246.
Row lengths are A072047.
Same as A319247 with rows reversed.
Composition of A000720 and A265668.
Looking at all numbers instead of just squarefree numbers gives A112798.
Sequence in context: A303945 A026793 A344089 * A239304 A072193 A233359
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Nov 18 2019
STATUS
approved