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A342192 Heinz numbers of partitions of crank 0.

%I A342192 #7 Apr 05 2021 09:19:03
%S A342192 6,10,14,22,26,34,38,46,58,62,74,82,86,94,100,106,118,122,134,140,142,
%T A342192 146,158,166,178,194,196,202,206,214,218,220,226,254,260,262,274,278,
%U A342192 298,300,302,308,314,326,334,340,346,358,362,364,380,382,386,394,398
%N A342192 Heinz numbers of partitions of crank 0.
%C A342192 The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). This gives a bijective correspondence between positive integers and integer partitions.
%C A342192 See A257989 or the program for a definition of crank of a partition.
%e A342192 The sequence of terms together with their prime indices begins:
%e A342192       6: {1,2}        106: {1,16}       218: {1,29}
%e A342192      10: {1,3}        118: {1,17}       220: {1,1,3,5}
%e A342192      14: {1,4}        122: {1,18}       226: {1,30}
%e A342192      22: {1,5}        134: {1,19}       254: {1,31}
%e A342192      26: {1,6}        140: {1,1,3,4}    260: {1,1,3,6}
%e A342192      34: {1,7}        142: {1,20}       262: {1,32}
%e A342192      38: {1,8}        146: {1,21}       274: {1,33}
%e A342192      46: {1,9}        158: {1,22}       278: {1,34}
%e A342192      58: {1,10}       166: {1,23}       298: {1,35}
%e A342192      62: {1,11}       178: {1,24}       300: {1,1,2,3,3}
%e A342192      74: {1,12}       194: {1,25}       302: {1,36}
%e A342192      82: {1,13}       196: {1,1,4,4}    308: {1,1,4,5}
%e A342192      86: {1,14}       202: {1,26}       314: {1,37}
%e A342192      94: {1,15}       206: {1,27}       326: {1,38}
%e A342192     100: {1,1,3,3}    214: {1,28}       334: {1,39}
%t A342192 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A342192 ck[y_]:=With[{w=Count[y,1]},If[w==0,Max@@y,Count[y,_?(#>w&)]-w]];
%t A342192 Select[Range[100],ck[primeMS[#]]==0&]
%Y A342192 Indices of zeros in A257989.
%Y A342192 A000005 counts constant partitions.
%Y A342192 A000041 counts partitions (strict: A000009).
%Y A342192 A001522 counts partitions of positive crank.
%Y A342192 A003242 counts anti-run compositions.
%Y A342192 A064391 counts partitions by crank.
%Y A342192 A064428 counts partitions of nonnegative crank.
%Y A342192 A224958 counts compositions with alternating parts unequal.
%Y A342192 A257989 gives the crank of the partition with Heinz number n.
%Y A342192 Cf. A000726, A008965, A056239, A112798, A124010, A130091, A325351, A325352.
%K A342192 nonn
%O A342192 1,1
%A A342192 _Gus Wiseman_, Apr 05 2021