This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370811 #12 May 24 2024 03:52:43
%S A370811 3,5,7,11,13,14,15,17,19,21,23,26,29,31,33,35,37,38,39,41,43,46,47,49,
%T A370811 51,53,55,57,58,59,61,65,67,69,70,71,73,74,77,78,79,83,85,86,87,89,91,
%U A370811 93,94,95,97,101,103,105,106,107,109,111,113,114,115,117,119
%N A370811 Numbers such that more than one set can be obtained by choosing a different divisor of each prime index.
%C A370811 A prime index of k is a number m such that prime(m) divides k. The multiset of prime indices of k is row k of A112798.
%e A370811 The prime indices of 70 are {1,3,4}, with choices (1,3,4) and (1,3,2), so 70 is in the sequence.
%e A370811 The terms together with their prime indices begin:
%e A370811 3: {2} 43: {14} 79: {22} 115: {3,9}
%e A370811 5: {3} 46: {1,9} 83: {23} 117: {2,2,6}
%e A370811 7: {4} 47: {15} 85: {3,7} 119: {4,7}
%e A370811 11: {5} 49: {4,4} 86: {1,14} 122: {1,18}
%e A370811 13: {6} 51: {2,7} 87: {2,10} 123: {2,13}
%e A370811 14: {1,4} 53: {16} 89: {24} 127: {31}
%e A370811 15: {2,3} 55: {3,5} 91: {4,6} 129: {2,14}
%e A370811 17: {7} 57: {2,8} 93: {2,11} 130: {1,3,6}
%e A370811 19: {8} 58: {1,10} 94: {1,15} 131: {32}
%e A370811 21: {2,4} 59: {17} 95: {3,8} 133: {4,8}
%e A370811 23: {9} 61: {18} 97: {25} 137: {33}
%e A370811 26: {1,6} 65: {3,6} 101: {26} 138: {1,2,9}
%e A370811 29: {10} 67: {19} 103: {27} 139: {34}
%e A370811 31: {11} 69: {2,9} 105: {2,3,4} 141: {2,15}
%e A370811 33: {2,5} 70: {1,3,4} 106: {1,16} 142: {1,20}
%e A370811 35: {3,4} 71: {20} 107: {28} 143: {5,6}
%e A370811 37: {12} 73: {21} 109: {29} 145: {3,10}
%e A370811 38: {1,8} 74: {1,12} 111: {2,12} 146: {1,21}
%e A370811 39: {2,6} 77: {4,5} 113: {30} 149: {35}
%e A370811 41: {13} 78: {1,2,6} 114: {1,2,8} 151: {36}
%t A370811 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n], {p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A370811 Select[Range[100],Length[Union[Sort /@ Select[Tuples[Divisors/@prix[#]],UnsameQ@@#&]]]>1&]
%Y A370811 For no choices we have A355740, counted by A370320.
%Y A370811 For at least one choice we have A368110, counted by A239312.
%Y A370811 Partitions of this type are counted by A370803.
%Y A370811 For a unique choice we have A370810, counted by A370595 and A370815.
%Y A370811 A000005 counts divisors.
%Y A370811 A006530 gives greatest prime factor, least A020639.
%Y A370811 A027746 lists prime factors, A112798 indices, length A001222.
%Y A370811 A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A370811 A355741, A355744, A355745 choose prime factors of prime indices.
%Y A370811 A370814 counts factorizations with choosable divisors, complement A370813.
%Y A370811 Cf. A133686, A355529, A355739, A355749, A367771, A367904, A370584, A370592, A370594, A370647, A370808, A370816.
%K A370811 nonn
%O A370811 1,1
%A A370811 _Gus Wiseman_, Mar 13 2024