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A338899
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Concatenated sequence of prime indices of squarefree semiprimes (A006881).
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46
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1, 2, 1, 3, 1, 4, 2, 3, 2, 4, 1, 5, 1, 6, 2, 5, 1, 7, 3, 4, 1, 8, 2, 6, 1, 9, 2, 7, 3, 5, 2, 8, 1, 10, 1, 11, 3, 6, 2, 9, 1, 12, 4, 5, 1, 13, 3, 7, 1, 14, 2, 10, 4, 6, 2, 11, 1, 15, 3, 8, 1, 16, 2, 12, 3, 9, 1, 17, 4, 7, 1, 18, 2, 13, 2, 14, 4, 8, 1, 19, 2, 15
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OFFSET
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1,2
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COMMENTS
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This is a triangle with two columns and strictly increasing rows, namely {A270650(n), A270652(n)}.
A squarefree semiprime is a product of any two distinct prime numbers. A prime index of n is a number m such that the m-th prime number divides n. The multiset of prime indices of n is row n of A112798.
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LINKS
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EXAMPLE
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The sequence of terms together with their prime indices begins:
6: {1,2} 57: {2,8} 106: {1,16} 155: {3,11}
10: {1,3} 58: {1,10} 111: {2,12} 158: {1,22}
14: {1,4} 62: {1,11} 115: {3,9} 159: {2,16}
15: {2,3} 65: {3,6} 118: {1,17} 161: {4,9}
21: {2,4} 69: {2,9} 119: {4,7} 166: {1,23}
22: {1,5} 74: {1,12} 122: {1,18} 177: {2,17}
26: {1,6} 77: {4,5} 123: {2,13} 178: {1,24}
33: {2,5} 82: {1,13} 129: {2,14} 183: {2,18}
34: {1,7} 85: {3,7} 133: {4,8} 185: {3,12}
35: {3,4} 86: {1,14} 134: {1,19} 187: {5,7}
38: {1,8} 87: {2,10} 141: {2,15} 194: {1,25}
39: {2,6} 91: {4,6} 142: {1,20} 201: {2,19}
46: {1,9} 93: {2,11} 143: {5,6} 202: {1,26}
51: {2,7} 94: {1,15} 145: {3,10} 203: {4,10}
55: {3,5} 95: {3,8} 146: {1,21} 205: {3,13}
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MATHEMATICA
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Join@@Cases[Select[Range[100], SquareFreeQ[#]&&PrimeOmega[#]==2&], k_:>PrimePi/@First/@FactorInteger[k]]
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CROSSREFS
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A320656 counts multiset partitions using these rows, or factorizations into squarefree semiprimes.
A338901 gives the row numbers for first appearances.
A004526 counts 2-part partitions, with strict case shifted right once.
A006881 lists squarefree semiprimes.
A046388 lists odd squarefree semiprimes.
A166237 gives first differences of squarefree semiprimes.
Cf. A030229, A056239, A065516, A112798, A115392, A167171, A176506, A320893, A338904, A338906, A338907, A338910, A338911.
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KEYWORD
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AUTHOR
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STATUS
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approved
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