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