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Greatest semiprime whose prime indices sum to n.
14

%I #10 Dec 06 2020 18:49:34

%S 4,6,10,15,25,35,55,77,121,143,187,221,289,323,391,493,551,667,841,

%T 899,1073,1189,1369,1517,1681,1763,1961,2183,2419,2537,2809,3127,3481,

%U 3599,3953,4189,4489,4757,5041,5293,5723,5963,6499,6887,7171,7663,8051,8633

%N Greatest semiprime whose prime indices sum to n.

%C 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 Robert Israel, <a href="/A339115/b339115.txt">Table of n, a(n) for n = 2..10000</a>

%e The sequence of terms together with their prime indices begins:

%e 4: {1,1} 493: {7,10} 2809: {16,16}

%e 6: {1,2} 551: {8,10} 3127: {16,17}

%e 10: {1,3} 667: {9,10} 3481: {17,17}

%e 15: {2,3} 841: {10,10} 3599: {17,18}

%e 25: {3,3} 899: {10,11} 3953: {17,19}

%e 35: {3,4} 1073: {10,12} 4189: {17,20}

%e 55: {3,5} 1189: {10,13} 4489: {19,19}

%e 77: {4,5} 1369: {12,12} 4757: {19,20}

%e 121: {5,5} 1517: {12,13} 5041: {20,20}

%e 143: {5,6} 1681: {13,13} 5293: {19,22}

%e 187: {5,7} 1763: {13,14} 5723: {17,25}

%e 221: {6,7} 1961: {12,16} 5963: {19,24}

%e 289: {7,7} 2183: {12,17} 6499: {19,25}

%e 323: {7,8} 2419: {13,17} 6887: {20,25}

%e 391: {7,9} 2537: {14,17} 7171: {20,26}

%p P:= [seq(ithprime(i),i=1..200)]:

%p [seq(max(seq(P[i]*P[j-i],i=1..j-1)),j=2..200)]; # _Robert Israel_, Dec 06 2020

%t Table[Max@@Table[Prime[k]*Prime[n-k],{k,n-1}],{n,2,30}]

%Y A024697 is the sum of the same semiprimes.

%Y A332765/A332877 is the squarefree case.

%Y A338904 has this sequence as row maxima.

%Y A339114 is the least among the same semiprimes.

%Y A001358 lists semiprimes, with odd/even terms A046315/A100484.

%Y A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.

%Y A037143 lists primes and semiprimes.

%Y A084126 and A084127 give the prime factors of semiprimes.

%Y A087112 groups semiprimes by greater factor.

%Y A320655 counts factorizations into semiprimes.

%Y A338898, A338912, and A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.

%Y A338899, A270650, and A270652 give the prime indices of squarefree semiprimes, with difference A338900.

%Y A338907/A338906 list semiprimes of odd/even weight.

%Y A338907/A338908 list squarefree semiprimes of odd/even weight.

%Y Cf. A000040, A001221, A001222, A014342, A025129, A056239, A062198, A098350, A112798, A338905, A339116.

%K nonn

%O 2,1

%A _Gus Wiseman_, Nov 28 2020