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 A344415 #8 May 21 2021 04:18:27
%S A344415 4,9,12,25,30,40,49,63,70,84,112,121,154,165,169,198,220,264,273,286,
%T A344415 289,325,351,352,361,364,390,442,468,520,529,561,595,624,646,714,741,
%U A344415 748,765,832,841,850,874,918,931,952,961,988,1020,1045,1173,1197,1224
%N A344415 Numbers whose greatest prime index is half their sum of prime indices.
%C A344415 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 A344415 A061395(a(n)) = A056239(a(n))/2.
%e A344415 The sequence of terms together with their prime indices begins:
%e A344415 4: {1,1} 198: {1,2,2,5}
%e A344415 9: {2,2} 220: {1,1,3,5}
%e A344415 12: {1,1,2} 264: {1,1,1,2,5}
%e A344415 25: {3,3} 273: {2,4,6}
%e A344415 30: {1,2,3} 286: {1,5,6}
%e A344415 40: {1,1,1,3} 289: {7,7}
%e A344415 49: {4,4} 325: {3,3,6}
%e A344415 63: {2,2,4} 351: {2,2,2,6}
%e A344415 70: {1,3,4} 352: {1,1,1,1,1,5}
%e A344415 84: {1,1,2,4} 361: {8,8}
%e A344415 112: {1,1,1,1,4} 364: {1,1,4,6}
%e A344415 121: {5,5} 390: {1,2,3,6}
%e A344415 154: {1,4,5} 442: {1,6,7}
%e A344415 165: {2,3,5} 468: {1,1,2,2,6}
%e A344415 169: {6,6} 520: {1,1,1,3,6}
%t A344415 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A344415 Select[Range[100],Max[primeMS[#]]==Total[primeMS[#]]/2&]
%Y A344415 The partitions with these Heinz numbers are counted by A035363.
%Y A344415 The conjugate version is A340387.
%Y A344415 This sequence is the case of equality in A344414 and A344416.
%Y A344415 A001222 counts prime factors with multiplicity.
%Y A344415 A025065 counts palindromic partitions, ranked by A265640.
%Y A344415 A027187 counts partitions of even length, ranked by A028260.
%Y A344415 A056239 adds up prime indices, row sums of A112798.
%Y A344415 A058696 counts partitions of even numbers, ranked by A300061.
%Y A344415 A301987 lists numbers whose sum of prime indices equals their product.
%Y A344415 A322109 ranks partitions of n with no part > n/2, counted by A110618.
%Y A344415 A334201 adds up all prime indices except the greatest.
%Y A344415 A344291 lists numbers m with A001222(m) <= A056239(m)/2, counted by A110618.
%Y A344415 A344296 lists numbers m with A001222(m) >= A056239(m)/2, counted by A025065.
%Y A344415 Cf. A000070, A001414, A209816, A301988, A316413, A316428, A320924, A325037, A325038, A325044, A330950, A344293, A344294, A344297.
%K A344415 nonn
%O A344415 1,1
%A A344415 _Gus Wiseman_, May 19 2021