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 A371179 #5 Mar 20 2024 21:53:35
%S A371179 3,5,7,9,11,13,14,15,17,19,21,23,25,26,27,28,29,31,33,35,37,38,39,41,
%T A371179 43,45,46,47,49,51,52,53,55,56,57,58,59,61,63,65,67,69,70,71,73,74,75,
%U A371179 76,77,78,79,81,83,85,86,87,89,91,92,93,94,95,97,98,99,101
%N A371179 Positive integers with fewer distinct prime factors (A001221) than distinct divisors of prime indices (A370820).
%C A371179 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 A371179 A001221(a(n)) < A370820(a(n)).
%e A371179 The terms together with their prime indices begin:
%e A371179 3: {2} 28: {1,1,4} 52: {1,1,6} 74: {1,12}
%e A371179 5: {3} 29: {10} 53: {16} 75: {2,3,3}
%e A371179 7: {4} 31: {11} 55: {3,5} 76: {1,1,8}
%e A371179 9: {2,2} 33: {2,5} 56: {1,1,1,4} 77: {4,5}
%e A371179 11: {5} 35: {3,4} 57: {2,8} 78: {1,2,6}
%e A371179 13: {6} 37: {12} 58: {1,10} 79: {22}
%e A371179 14: {1,4} 38: {1,8} 59: {17} 81: {2,2,2,2}
%e A371179 15: {2,3} 39: {2,6} 61: {18} 83: {23}
%e A371179 17: {7} 41: {13} 63: {2,2,4} 85: {3,7}
%e A371179 19: {8} 43: {14} 65: {3,6} 86: {1,14}
%e A371179 21: {2,4} 45: {2,2,3} 67: {19} 87: {2,10}
%e A371179 23: {9} 46: {1,9} 69: {2,9} 89: {24}
%e A371179 25: {3,3} 47: {15} 70: {1,3,4} 91: {4,6}
%e A371179 26: {1,6} 49: {4,4} 71: {20} 92: {1,1,9}
%e A371179 27: {2,2,2} 51: {2,7} 73: {21} 93: {2,11}
%t A371179 Select[Range[100],PrimeNu[#]<Length[Union @@ Divisors/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]]&]
%Y A371179 The LHS is A001221, distinct case of A001222.
%Y A371179 The RHS is A370820, for prime factors A303975.
%Y A371179 Partitions of this type are counted by A371132, strict A371180.
%Y A371179 Counting all prime indices on the LHS gives A371168, counted by A371173.
%Y A371179 The complement is A371177, counted by A371178, strict A371128.
%Y A371179 A000005 counts divisors.
%Y A371179 A000041 counts integer partitions, strict A000009.
%Y A371179 A008284 counts partitions by length.
%Y A371179 A305148 counts pairwise indivisible (stable) partitions, ranks A316476.
%Y A371179 Cf. A003963, A239312, A285573, A355529, A370802, A370803, A371130, A371165, A371171, A371172.
%K A371179 nonn
%O A371179 1,1
%A A371179 _Gus Wiseman_, Mar 19 2024