cp's OEIS Frontend

A379844 Squarefree numbers x such that the product of prime indices of x is a multiple of the sum of prime indices of x.

%I A379844 #10 Jan 20 2025 09:11:12
%S A379844 2,3,5,7,11,13,17,19,23,29,30,31,37,41,43,47,53,59,61,65,67,71,73,79,
%T A379844 83,89,97,101,103,107,109,113,127,131,137,139,149,151,154,157,163,165,
%U A379844 167,173,179,181,190,191,193,197,199,211,223,227,229,233,239,241
%N A379844 Squarefree numbers x such that the product of prime indices of x is a multiple of the sum of prime indices of x.
%C A379844 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. The sum and product of prime indices are A056239 and A003963 respectively.
%F A379844 Satisfies A056239(a(n))|A003963(a(n)).
%t A379844 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A379844 Select[Range[2,100],SquareFreeQ[#]&&Divisible[Times@@prix[#],Plus@@prix[#]]&]
%Y A379844 Squarefree case of A326149.
%Y A379844 For nonprime instead of squarefree we have A326150.
%Y A379844 The non-prime case is A326158.
%Y A379844 Partitions of this type are counted by A379733, see A379735.
%Y A379844 The even case is A379845, counted by A380221.
%Y A379844 A003963 multiplies together prime indices.
%Y A379844 A005117 lists the squarefree numbers.
%Y A379844 A056239 adds up prime indices.
%Y A379844 Counting and ranking multisets by comparing sum and product:
%Y A379844 - same: A001055, ranks A301987
%Y A379844 - divisible: A057567, ranks A326155
%Y A379844 - divisor: A057568, ranks A326149
%Y A379844 - greater than: A096276 shifted right, ranks A325038
%Y A379844 - greater or equal: A096276, ranks A325044
%Y A379844 - less than: A114324, ranks A325037, see A318029, A379720
%Y A379844 - less or equal: A319005, ranks A379721, see A025147
%Y A379844 - different: A379736, ranks A379722, see A111133
%Y A379844 Cf. A000720, A001222, A036844, A112798, A324850, A324851, A324925, A326151, A326153/A326154, A326156, A326157.
%K A379844 nonn
%O A379844 1,1
%A A379844 _Gus Wiseman_, Jan 19 2025