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 A371170 #8 Mar 18 2024 11:45:31
%S A371170 1,2,3,5,6,7,9,10,11,13,14,15,17,19,21,22,23,25,26,28,29,30,31,33,34,
%T A371170 35,37,38,39,41,42,43,45,46,47,49,51,52,53,55,57,58,59,61,62,63,65,66,
%U A371170 67,69,70,71,73,74,75,76,77,78,79,82,83,85,86,87,89,91,92
%N A371170 Positive integers with at most as many prime factors (A001222) as distinct divisors of prime indices (A370820).
%C A371170 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.
%e A371170 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 A371170 The terms together with their prime indices begin:
%e A371170 1: {} 22: {1,5} 42: {1,2,4} 63: {2,2,4}
%e A371170 2: {1} 23: {9} 43: {14} 65: {3,6}
%e A371170 3: {2} 25: {3,3} 45: {2,2,3} 66: {1,2,5}
%e A371170 5: {3} 26: {1,6} 46: {1,9} 67: {19}
%e A371170 6: {1,2} 28: {1,1,4} 47: {15} 69: {2,9}
%e A371170 7: {4} 29: {10} 49: {4,4} 70: {1,3,4}
%e A371170 9: {2,2} 30: {1,2,3} 51: {2,7} 71: {20}
%e A371170 10: {1,3} 31: {11} 52: {1,1,6} 73: {21}
%e A371170 11: {5} 33: {2,5} 53: {16} 74: {1,12}
%e A371170 13: {6} 34: {1,7} 55: {3,5} 75: {2,3,3}
%e A371170 14: {1,4} 35: {3,4} 57: {2,8} 76: {1,1,8}
%e A371170 15: {2,3} 37: {12} 58: {1,10} 77: {4,5}
%e A371170 17: {7} 38: {1,8} 59: {17} 78: {1,2,6}
%e A371170 19: {8} 39: {2,6} 61: {18} 79: {22}
%e A371170 21: {2,4} 41: {13} 62: {1,11} 82: {1,13}
%t A371170 Select[Range[100],PrimeOmega[#]<=Length[Union @@ Divisors/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]]&]
%Y A371170 The complement is A370348, counted by A371171.
%Y A371170 The case of equality is A370802, counted by A371130, strict A371128.
%Y A371170 The RHS is A370820, for prime factors instead of divisors A303975.
%Y A371170 The strict version is A371168 counted by A371173.
%Y A371170 The opposite version is A371169.
%Y A371170 Choosable partitions: A239312 (A368110), A355740 (A370320), A370592 (A368100), A370593 (A355529).
%Y A371170 A000005 counts divisors.
%Y A371170 A001221 counts distinct prime factors.
%Y A371170 A027746 lists prime factors, indices A112798, length A001222.
%Y A371170 A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A371170 Cf. A003963, A319899, A355737, A355739, A355741, A370808, A371127.
%K A371170 nonn
%O A371170 1,2
%A A371170 _Gus Wiseman_, Mar 16 2024