cp's OEIS Frontend

A379845 Even squarefree numbers x such that the product of prime indices of x is a multiple of the sum of prime indices of x.

%I A379845 #6 Jan 20 2025 09:10:41
%S A379845 2,30,154,190,390,442,506,658,714,874,1110,1118,1254,1330,1430,1786,
%T A379845 1794,1798,1958,2310,2414,2442,2470,2730,2958,3034,3066,3266,3390,
%U A379845 3534,3710,3770,3874,3914,4042,4466,4526,4758,4930,5106,5434,5474,5642,6090,6106
%N A379845 Even squarefree numbers x such that the product of prime indices of x is a multiple of the sum of prime indices of x.
%C A379845 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.
%e A379845 The terms together with their prime indices begin:
%e A379845      2: {1}
%e A379845     30: {1,2,3}
%e A379845    154: {1,4,5}
%e A379845    190: {1,3,8}
%e A379845    390: {1,2,3,6}
%e A379845    442: {1,6,7}
%e A379845    506: {1,5,9}
%e A379845    658: {1,4,15}
%e A379845    714: {1,2,4,7}
%e A379845    874: {1,8,9}
%e A379845   1110: {1,2,3,12}
%t A379845 Select[Range[2,1000],EvenQ[#]&&SquareFreeQ[#]&&Divisible[Times@@prix[#],Plus@@prix[#]]&]
%Y A379845 Even squarefree case of A326149.
%Y A379845 For nonprime instead of even we have A326158.
%Y A379845 Squarefree case of A379319.
%Y A379845 Even case of A379844.
%Y A379845 Partitions of this type are counted by A380221, see A379733, A379735.
%Y A379845 A003963 multiplies together prime indices.
%Y A379845 A005117 lists the squarefree numbers.
%Y A379845 A056239 adds up prime indices.
%Y A379845 Counting and ranking multisets by comparing sum and product:
%Y A379845 - same: A001055, ranks A301987
%Y A379845 - multiple: A057567, ranks A326155
%Y A379845 - divisor: A057568, ranks A326149
%Y A379845 - greater than: A096276 shifted right, ranks A325038
%Y A379845 - greater or equal: A096276, ranks A325044
%Y A379845 - less than: A114324, ranks A325037, see A318029, A379720
%Y A379845 - less or equal: A319005, ranks A379721, see A025147
%Y A379845 - different: A379736, ranks A379722, see A111133
%Y A379845 Cf. A000720, A001222, A112798, A175508, A324850, A324851, A326150, A326151, A326153/A326154, A326156, A326157.
%K A379845 nonn
%O A379845 1,1
%A A379845 _Gus Wiseman_, Jan 20 2025