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A339115 Greatest semiprime whose prime indices sum to n.

%I A339115 #10 Dec 06 2020 18:49:34
%S A339115 4,6,10,15,25,35,55,77,121,143,187,221,289,323,391,493,551,667,841,
%T A339115 899,1073,1189,1369,1517,1681,1763,1961,2183,2419,2537,2809,3127,3481,
%U A339115 3599,3953,4189,4489,4757,5041,5293,5723,5963,6499,6887,7171,7663,8051,8633
%N A339115 Greatest semiprime whose prime indices sum to n.
%C A339115 A semiprime is a product of any two prime numbers. A prime index of n is a number m such that the m-th prime number divides n. The multiset of prime indices of n is row n of A112798.
%H A339115 Robert Israel, <a href="/A339115/b339115.txt">Table of n, a(n) for n = 2..10000</a>
%e A339115 The sequence of terms together with their prime indices begins:
%e A339115         4: {1,1}      493: {7,10}      2809: {16,16}
%e A339115         6: {1,2}      551: {8,10}      3127: {16,17}
%e A339115        10: {1,3}      667: {9,10}      3481: {17,17}
%e A339115        15: {2,3}      841: {10,10}     3599: {17,18}
%e A339115        25: {3,3}      899: {10,11}     3953: {17,19}
%e A339115        35: {3,4}     1073: {10,12}     4189: {17,20}
%e A339115        55: {3,5}     1189: {10,13}     4489: {19,19}
%e A339115        77: {4,5}     1369: {12,12}     4757: {19,20}
%e A339115       121: {5,5}     1517: {12,13}     5041: {20,20}
%e A339115       143: {5,6}     1681: {13,13}     5293: {19,22}
%e A339115       187: {5,7}     1763: {13,14}     5723: {17,25}
%e A339115       221: {6,7}     1961: {12,16}     5963: {19,24}
%e A339115       289: {7,7}     2183: {12,17}     6499: {19,25}
%e A339115       323: {7,8}     2419: {13,17}     6887: {20,25}
%e A339115       391: {7,9}     2537: {14,17}     7171: {20,26}
%p A339115 P:= [seq(ithprime(i),i=1..200)]:
%p A339115 [seq(max(seq(P[i]*P[j-i],i=1..j-1)),j=2..200)]; # _Robert Israel_, Dec 06 2020
%t A339115 Table[Max@@Table[Prime[k]*Prime[n-k],{k,n-1}],{n,2,30}]
%Y A339115 A024697 is the sum of the same semiprimes.
%Y A339115 A332765/A332877 is the squarefree case.
%Y A339115 A338904 has this sequence as row maxima.
%Y A339115 A339114 is the least among the same semiprimes.
%Y A339115 A001358 lists semiprimes, with odd/even terms A046315/A100484.
%Y A339115 A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A339115 A037143 lists primes and semiprimes.
%Y A339115 A084126 and A084127 give the prime factors of semiprimes.
%Y A339115 A087112 groups semiprimes by greater factor.
%Y A339115 A320655 counts factorizations into semiprimes.
%Y A339115 A338898, A338912, and A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
%Y A339115 A338899, A270650, and A270652 give the prime indices of squarefree semiprimes, with difference A338900.
%Y A339115 A338907/A338906 list semiprimes of odd/even weight.
%Y A339115 A338907/A338908 list squarefree semiprimes of odd/even weight.
%Y A339115 Cf. A000040, A001221, A001222, A014342, A025129, A056239, A062198, A098350, A112798, A338905, A339116.
%K A339115 nonn
%O A339115 2,1
%A A339115 _Gus Wiseman_, Nov 28 2020