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%I #7 Apr 13 2019 22:16:45
%S 3,10,15,25,28,42,63,70,88,98,105,132,147,175,198,208,220,245,297,308,
%T 312,330,343,462,468,484,495,520,544,550,693,702,726,728,770,780,816,
%U 825,1053,1078,1089,1092,1144,1155,1170,1210,1216,1224,1300,1352,1360
%N Heinz numbers of integer partitions with Dyson rank 1.
%C Numbers whose maximum prime index is one greater than their number of prime indices counted with multiplicity.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H FindStat, <a href="http://www.findstat.org/StatisticsDatabase/St000145">St000145: The Dyson rank of a partition</a>
%e The sequence of terms together with their prime indices begins:
%e 3: {2}
%e 10: {1,3}
%e 15: {2,3}
%e 25: {3,3}
%e 28: {1,1,4}
%e 42: {1,2,4}
%e 63: {2,2,4}
%e 70: {1,3,4}
%e 88: {1,1,1,5}
%e 98: {1,4,4}
%e 105: {2,3,4}
%e 132: {1,1,2,5}
%e 147: {2,4,4}
%e 175: {3,3,4}
%e 198: {1,2,2,5}
%e 208: {1,1,1,1,6}
%e 220: {1,1,3,5}
%e 245: {3,4,4}
%e 297: {2,2,2,5}
%e 308: {1,1,4,5}
%t Select[Range[1000],PrimePi[FactorInteger[#][[-1,1]]]-PrimeOmega[#]==1&]
%Y Positions of 1's in A257541.
%Y Cf. A001222, A047993, A056239, A061395, A063995, A101198, A106529, A112798, A257990, A263297, A325225, A325234, A325235.
%K nonn
%O 1,1
%A _Gus Wiseman_, Apr 13 2019
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