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 A371168 #6 Mar 16 2024 21:41:30
%S A371168 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 A371168 51,52,53,55,57,58,59,61,65,67,69,70,71,73,74,76,77,78,79,83,85,86,87,
%U A371168 89,91,93,94,95,97,101,103,105,106,107,109,111,113,114,115
%N A371168 Positive integers with fewer prime factors (A001222) than distinct divisors of prime indices (A370820).
%C A371168 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.
%F A371168 A001222(a(n)) < A370820(a(n)).
%e A371168 The prime indices of 105 are {2,3,4}, and there are 3 prime factors (3,5,7) and 4 distinct divisors of prime indices (1,2,3,4), so 105 is in the sequence.
%e A371168 The terms together with their prime indices begin:
%e A371168 3: {2} 35: {3,4} 59: {17} 86: {1,14}
%e A371168 5: {3} 37: {12} 61: {18} 87: {2,10}
%e A371168 7: {4} 38: {1,8} 65: {3,6} 89: {24}
%e A371168 11: {5} 39: {2,6} 67: {19} 91: {4,6}
%e A371168 13: {6} 41: {13} 69: {2,9} 93: {2,11}
%e A371168 14: {1,4} 43: {14} 70: {1,3,4} 94: {1,15}
%e A371168 15: {2,3} 46: {1,9} 71: {20} 95: {3,8}
%e A371168 17: {7} 47: {15} 73: {21} 97: {25}
%e A371168 19: {8} 49: {4,4} 74: {1,12} 101: {26}
%e A371168 21: {2,4} 51: {2,7} 76: {1,1,8} 103: {27}
%e A371168 23: {9} 52: {1,1,6} 77: {4,5} 105: {2,3,4}
%e A371168 26: {1,6} 53: {16} 78: {1,2,6} 106: {1,16}
%e A371168 29: {10} 55: {3,5} 79: {22} 107: {28}
%e A371168 31: {11} 57: {2,8} 83: {23} 109: {29}
%e A371168 33: {2,5} 58: {1,10} 85: {3,7} 111: {2,12}
%t A371168 Select[Range[100],PrimeOmega[#]<Length[Union @@ Divisors/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]]&]
%Y A371168 The opposite version is A370348 counted by A371171.
%Y A371168 The version for equality is A370802, counted by A371130, strict A371128.
%Y A371168 The RHS is A370820, for prime factors instead of divisors A303975.
%Y A371168 For divisors instead of prime factors on the LHS we get A371166.
%Y A371168 The complement is counted by A371169.
%Y A371168 The weak version is A371170.
%Y A371168 Partitions of this type are counted by A371173.
%Y A371168 Choosable partitions: A239312 (A368110), A355740 (A370320), A370592 (A368100), A370593 (A355529).
%Y A371168 A000005 counts divisors.
%Y A371168 A001221 counts distinct prime factors.
%Y A371168 A027746 lists prime factors, indices A112798, length A001222.
%Y A371168 A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A371168 Cf. A003963, A319899, A355737, A355739, A355741, A370808, A370814, A371127.
%K A371168 nonn
%O A371168 1,1
%A A371168 _Gus Wiseman_, Mar 16 2024