|
|
A339115
|
|
Greatest semiprime whose prime indices sum to n.
|
|
14
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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.
A338904 has this sequence as row maxima.
A339114 is the least among the same semiprimes.
A037143 lists primes and semiprimes.
A087112 groups semiprimes by greater factor.
A320655 counts factorizations into semiprimes.
Cf. A000040, A001221, A001222, A014342, A025129, A056239, A062198, A098350, A112798, A338905, A339116.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|