cp's OEIS Frontend

A383015 Numbers whose prime indices have more than one permutation with all equal run-sums.

%I A383015 #9 Apr 17 2025 23:21:03
%S A383015 12,40,63,112,144,325,351,352,675,832,931,1008,1539,1600,1728,2176,
%T A383015 2875,3509,3969,4864,6253,7047,7056,8775,9072,11776,12427,12544,12691,
%U A383015 16128,19133,20736,20800,22464,23125,26973,29403,29696,32269,43200,49392,57967,59711
%N A383015 Numbers whose prime indices have more than one permutation with all equal run-sums.
%C A383015 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, sum A056239.
%C A383015 All terms appear to have even sum of prime indices.
%e A383015 The terms together with their prime indices begin:
%e A383015      12: {1,1,2}
%e A383015      40: {1,1,1,3}
%e A383015      63: {2,2,4}
%e A383015     112: {1,1,1,1,4}
%e A383015     144: {1,1,1,1,2,2}
%e A383015     325: {3,3,6}
%e A383015     351: {2,2,2,6}
%e A383015     352: {1,1,1,1,1,5}
%e A383015     675: {2,2,2,3,3}
%e A383015     832: {1,1,1,1,1,1,6}
%e A383015     931: {4,4,8}
%e A383015    1008: {1,1,1,1,2,2,4}
%e A383015    1539: {2,2,2,2,8}
%e A383015    1600: {1,1,1,1,1,1,3,3}
%e A383015    1728: {1,1,1,1,1,1,2,2,2}
%t A383015 Select[Range[100],Length[Select[Permutations[PrimePi/@Join@@ConstantArray@@@FactorInteger[#]],SameQ@@Total/@Split[#]&]]>1&]
%Y A383015 Compositions of this type are counted by A353851, ranked by A353848.
%Y A383015 Positions of terms > 1 in A382877, zeros A383100 (complement A383014).
%Y A383015 For run-lengths instead of sums we have A383089, counted by A383090.
%Y A383015 The complement for run-lengths instead of sums is A383091, counted by A383092
%Y A383015 Partitions of this type are counted by A383097.
%Y A383015 A044813 lists numbers whose binary expansion has distinct run-lengths.
%Y A383015 A056239 adds up prime indices, row sums of A112798.
%Y A383015 A304442 counts compositions with equal run-sums, complement A382076.
%Y A383015 A329739 counts compositions with distinct run-lengths, ranks A351596.
%Y A383015 A353837 counts partitions with distinct run-sums, ranks A353838.
%Y A383015 A353847 gives composition run-sum transformation, for partitions A353832.
%Y A383015 A353932 lists run-sums of standard compositions.
%Y A383015 Cf. A000720, A000961, A001221, A001222, A329738, A353833, A354584, A381636, A381871, A382857, A382876, A382879.
%K A383015 nonn
%O A383015 1,1
%A A383015 _Gus Wiseman_, Apr 14 2025