A339115 Greatest semiprime whose prime indices sum to n.

4, 6, 10, 15, 25, 35, 55, 77, 121, 143, 187, 221, 289, 323, 391, 493, 551, 667, 841, 899, 1073, 1189, 1369, 1517, 1681, 1763, 1961, 2183, 2419, 2537, 2809, 3127, 3481, 3599, 3953, 4189, 4489, 4757, 5041, 5293, 5723, 5963, 6499, 6887, 7171, 7663, 8051, 8633

Offset

2,1

Comments

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.

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Example

The sequence of terms together with their prime indices begins:
        4: {1,1}      493: {7,10}      2809: {16,16}
        6: {1,2}      551: {8,10}      3127: {16,17}
       10: {1,3}      667: {9,10}      3481: {17,17}
       15: {2,3}      841: {10,10}     3599: {17,18}
       25: {3,3}      899: {10,11}     3953: {17,19}
       35: {3,4}     1073: {10,12}     4189: {17,20}
       55: {3,5}     1189: {10,13}     4489: {19,19}
       77: {4,5}     1369: {12,12}     4757: {19,20}
      121: {5,5}     1517: {12,13}     5041: {20,20}
      143: {5,6}     1681: {13,13}     5293: {19,22}
      187: {5,7}     1763: {13,14}     5723: {17,25}
      221: {6,7}     1961: {12,16}     5963: {19,24}
      289: {7,7}     2183: {12,17}     6499: {19,25}
      323: {7,8}     2419: {13,17}     6887: {20,25}
      391: {7,9}     2537: {14,17}     7171: {20,26}

Maple

P:= [seq(ithprime(i), i=1..200)]:
[seq(max(seq(P[i]*P[j-i], i=1..j-1)), j=2..200)]; # Robert Israel, Dec 06 2020

Mathematica

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

Crossrefs

A024697 is the sum of the same semiprimes.

A332765/A332877 is the squarefree case.

A338904 has this sequence as row maxima.

A339114 is the least among the same semiprimes.

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

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

A037143 lists primes and semiprimes.

A084126 and A084127 give the prime factors of semiprimes.

A087112 groups semiprimes by greater factor.

A320655 counts factorizations into semiprimes.

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

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

A338907/A338906 list semiprimes of odd/even weight.

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

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

Sequence in context: A004399 A247558 A373630 * A217836 A215232 A186777

Adjacent sequences: A339112 A339113 A339114 * A339116 A339117 A339118

Keyword

nonn

Author

Gus Wiseman, Nov 28 2020

Status

approved