cp's OEIS Frontend

A339114 Least semiprime whose prime indices sum to n.

%I A339114 #13 Sep 06 2022 10:38:12
%S A339114 4,6,9,14,21,26,34,38,46,58,62,74,82,86,94,106,118,122,134,142,146,
%T A339114 158,166,178,194,202,206,214,218,226,254,262,274,278,298,302,314,326,
%U A339114 334,346,358,362,382,386,394,398,422,446,454,458,466,478,482,502,514,526
%N A339114 Least semiprime whose prime indices sum to n.
%C A339114 Converges to A100484.
%C A339114 After a(4) = 9, also the least squarefree semiprime whose prime indices sum to n.
%C A339114 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.
%e A339114 The sequence of terms together with their prime indices begins:
%e A339114       4: {1,1}     106: {1,16}    254: {1,31}
%e A339114       6: {1,2}     118: {1,17}    262: {1,32}
%e A339114       9: {2,2}     122: {1,18}    274: {1,33}
%e A339114      14: {1,4}     134: {1,19}    278: {1,34}
%e A339114      21: {2,4}     142: {1,20}    298: {1,35}
%e A339114      26: {1,6}     146: {1,21}    302: {1,36}
%e A339114      34: {1,7}     158: {1,22}    314: {1,37}
%e A339114      38: {1,8}     166: {1,23}    326: {1,38}
%e A339114      46: {1,9}     178: {1,24}    334: {1,39}
%e A339114      58: {1,10}    194: {1,25}    346: {1,40}
%e A339114      62: {1,11}    202: {1,26}    358: {1,41}
%e A339114      74: {1,12}    206: {1,27}    362: {1,42}
%e A339114      82: {1,13}    214: {1,28}    382: {1,43}
%e A339114      86: {1,14}    218: {1,29}    386: {1,44}
%e A339114      94: {1,15}    226: {1,30}    394: {1,45}
%t A339114 Table[Min@@Table[Prime[k]*Prime[n-k],{k,n-1}],{n,2,30}]
%t A339114 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 *)
%o A339114 (PARI) a(n) = vecmin(vector(n-1, k, prime(k)*prime(n-k))); \\ _Michel Marcus_, Dec 03 2020
%Y A339114 A024697 is the sum of the same semiprimes.
%Y A339114 A098350 has this sequence as antidiagonal minima.
%Y A339114 A338904 has this sequence as row minima.
%Y A339114 A339114 (this sequence) is the squarefree case for n > 4.
%Y A339114 A339115 is the greatest among the same semiprimes.
%Y A339114 A001358 lists semiprimes, with odd/even terms A046315/A100484.
%Y A339114 A006881 lists squarefree semiprimes, with odd/even terms A046388/A100484.
%Y A339114 A037143 lists primes and semiprimes.
%Y A339114 A056239 gives the sum of prime indices of n.
%Y A339114 A084126 and A084127 give the prime factors of semiprimes.
%Y A339114 A087112 groups semiprimes by greater factor.
%Y A339114 A320655 counts factorizations into semiprimes.
%Y A339114 A332765/A332877 is the greatest squarefree semiprime of weight n.
%Y A339114 A338898, A338912, and A338913 give the prime indices of semiprimes, with product A087794, sum A176504, and difference A176506.
%Y A339114 A338899, A270650, and A270652 give the prime indices of squarefree semiprimes, with difference A338900.
%Y A339114 A338907/A338906 list semiprimes of odd/even weight.
%Y A339114 A338907/A338908 list squarefree semiprimes of odd/even weight.
%Y A339114 Cf. A000040, A001221, A001222, A014342, A025129, A062198, A112798, A338905, A339116.
%K A339114 nonn
%O A339114 2,1
%A A339114 _Gus Wiseman_, Nov 28 2020