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%I #6 Apr 13 2019 22:16:59
%S 3,4,10,12,15,18,25,27,28,40,42,60,63,70,88,90,98,100,105,112,132,135,
%T 147,150,168,175,198,208,220,225,245,250,252,280,297,308,312,330,343,
%U 352,375,378,392,420,462,468,484,495,520,528,544,550,567,588,625,630
%N Heinz numbers of integer partitions with Dyson rank 1 or -1.
%C Numbers whose maximum prime index and number of prime indices counted with multiplicity differ by 1.
%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 4: {1,1}
%e 10: {1,3}
%e 12: {1,1,2}
%e 15: {2,3}
%e 18: {1,2,2}
%e 25: {3,3}
%e 27: {2,2,2}
%e 28: {1,1,4}
%e 40: {1,1,1,3}
%e 42: {1,2,4}
%e 60: {1,1,2,3}
%e 63: {2,2,4}
%e 70: {1,3,4}
%e 88: {1,1,1,5}
%e 90: {1,2,2,3}
%e 98: {1,4,4}
%e 100: {1,1,3,3}
%e 105: {2,3,4}
%e 112: {1,1,1,1,4}
%t Select[Range[1000],Abs[PrimePi[FactorInteger[#][[-1,1]]]-PrimeOmega[#]]==1&]
%Y Positions of 1's and -1's in A257541.
%Y Cf. A001222, A047993, A056239, A061395, A063995, A101198, A106529, A112798, A257990, A263297, A325225, A325233, A325234.
%K nonn
%O 1,1
%A _Gus Wiseman_, Apr 13 2019
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