cp's OEIS Frontend

A371169 Positive integers with at least as many prime factors (A001222) as distinct divisors of prime indices (A370820).

%I A371169 #6 Mar 16 2024 21:40:54
%S A371169 1,2,4,6,8,9,10,12,16,18,20,22,24,25,27,28,30,32,34,36,40,42,44,45,48,
%T A371169 50,54,56,60,62,63,64,66,68,72,75,80,81,82,84,88,90,92,96,98,99,100,
%U A371169 102,104,108,110,112,118,120,121,124,125,126,128,132,134,135
%N A371169 Positive integers with at least as many prime factors (A001222) as distinct divisors of prime indices (A370820).
%C A371169 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 A371169 The terms together with their prime indices begin:
%e A371169      1: {}
%e A371169      2: {1}
%e A371169      4: {1,1}
%e A371169      6: {1,2}
%e A371169      8: {1,1,1}
%e A371169      9: {2,2}
%e A371169     10: {1,3}
%e A371169     12: {1,1,2}
%e A371169     16: {1,1,1,1}
%e A371169     18: {1,2,2}
%e A371169     20: {1,1,3}
%e A371169     22: {1,5}
%e A371169     24: {1,1,1,2}
%e A371169     25: {3,3}
%e A371169     27: {2,2,2}
%e A371169     28: {1,1,4}
%e A371169     30: {1,2,3}
%e A371169     32: {1,1,1,1,1}
%e A371169     34: {1,7}
%e A371169     36: {1,1,2,2}
%t A371169 Select[Range[100],PrimeOmega[#]>=Length[Union @@ Divisors/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]]&]
%Y A371169 The strict version is A370348 counted by A371171.
%Y A371169 The case of equality is A370802, counted by A371130, strict A371128.
%Y A371169 The RHS is A370820, for prime factors instead of divisors A303975.
%Y A371169 The complement is A371168, counted by A371173.
%Y A371169 The opposite version is A371170.
%Y A371169 The version for prime factors instead of divisors on the RHS is A319899.
%Y A371169 Choosable partitions: A239312 (A368110), A355740 (A370320), A370592 (A368100), A370593 (A355529).
%Y A371169 A000005 counts divisors.
%Y A371169 A001221 counts distinct prime factors.
%Y A371169 A027746 lists prime factors, indices A112798, length A001222.
%Y A371169 A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A371169 Cf. A003963, A355737, A355739, A355741, A370808, A370813, A370814, A371127.
%K A371169 nonn
%O A371169 1,2
%A A371169 _Gus Wiseman_, Mar 16 2024