A339114 Least semiprime whose prime indices sum to n.

4, 6, 9, 14, 21, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 386, 394, 398, 422, 446, 454, 458, 466, 478, 482, 502, 514, 526

Offset

2,1

Comments

Converges to A100484.

After a(4) = 9, also the least squarefree semiprime whose prime indices sum to n.

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

Table of n, a(n) for n=2..57.

Example

The sequence of terms together with their prime indices begins:
      4: {1,1}     106: {1,16}    254: {1,31}
      6: {1,2}     118: {1,17}    262: {1,32}
      9: {2,2}     122: {1,18}    274: {1,33}
     14: {1,4}     134: {1,19}    278: {1,34}
     21: {2,4}     142: {1,20}    298: {1,35}
     26: {1,6}     146: {1,21}    302: {1,36}
     34: {1,7}     158: {1,22}    314: {1,37}
     38: {1,8}     166: {1,23}    326: {1,38}
     46: {1,9}     178: {1,24}    334: {1,39}
     58: {1,10}    194: {1,25}    346: {1,40}
     62: {1,11}    202: {1,26}    358: {1,41}
     74: {1,12}    206: {1,27}    362: {1,42}
     82: {1,13}    214: {1,28}    382: {1,43}
     86: {1,14}    218: {1,29}    386: {1,44}
     94: {1,15}    226: {1,30}    394: {1,45}

Mathematica

Table[Min@@Table[Prime[k]*Prime[n-k], {k, n-1}], {n, 2, 30}]
Take[DeleteDuplicates[SortBy[{Times@@#, Total[PrimePi[#]]}&/@Tuples[ Prime[ Range[ 200]], 2], {Last, First}], GreaterEqual[#1[[2]], #2[[2]]]&][[All, 1]], 60] (* Harvey P. Dale, Sep 06 2022 *)

Prog

(PARI) a(n) = vecmin(vector(n-1, k, prime(k)*prime(n-k))); \\ Michel Marcus, Dec 03 2020

Crossrefs

A024697 is the sum of the same semiprimes.

A098350 has this sequence as antidiagonal minima.

A338904 has this sequence as row minima.

A339114 (this sequence) is the squarefree case for n > 4.

A339115 is the greatest 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.

A056239 gives the sum of prime indices of n.

A084126 and A084127 give the prime factors of semiprimes.

A087112 groups semiprimes by greater factor.

A320655 counts factorizations into semiprimes.

A332765/A332877 is the greatest squarefree semiprime of weight n.

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, A062198, A112798, A338905, A339116.

Sequence in context: A330071 A057988 A175587 * A175709 A073679 A257559

Adjacent sequences: A339111 A339112 A339113 * A339115 A339116 A339117

Keyword

nonn

Author

Gus Wiseman, Nov 28 2020

Status

approved