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A347047 Smallest squarefree semiprime whose prime indices sum to n.

%I A347047 #22 Sep 15 2021 00:28:00
%S A347047 6,10,14,21,26,34,38,46,58,62,74,82,86,94,106,118,122,134,142,146,158,
%T A347047 166,178,194,202,206,214,218,226,254,262,274,278,298,302,314,326,334,
%U A347047 346,358,362,382,386,394,398,422,446,454,458,466,478,482,502,514,526
%N A347047 Smallest squarefree semiprime whose prime indices sum to n.
%C A347047 Compared to A001747, we have 21 instead of 22 and lack 2 and 4.
%C A347047 Compared to A100484 (shifted) we have 21 instead of 22 and lack 4.
%C A347047 Compared to A161344, we have 21 instead of 22 and lack 4 and 8.
%C A347047 Compared to A339114, we have 11 instead of 9 and lack 4.
%C A347047 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A347047 A squarefree semiprime (A006881) is a product of any two distinct prime numbers.
%e A347047 The initial terms and their prime indices:
%e A347047     6: {1,2}
%e A347047    10: {1,3}
%e A347047    14: {1,4}
%e A347047    21: {2,4}
%e A347047    26: {1,6}
%e A347047    34: {1,7}
%e A347047    38: {1,8}
%e A347047    46: {1,9}
%t A347047 Table[Min@@Select[Table[Times@@Prime/@y,{y,IntegerPartitions[n,{2}]}],SquareFreeQ],{n,3,50}]
%o A347047 (Python)
%o A347047 from sympy import prime, sieve
%o A347047 def a(n):
%o A347047     p = [0] + list(sieve.primerange(1, prime(n)+1))
%o A347047     return min(p[i]*p[n-i] for i in range(1, (n+1)//2))
%o A347047 print([a(n) for n in range(3, 58)]) # _Michael S. Branicky_, Sep 05 2021
%Y A347047 The opposite version (greatest instead of smallest) is A332765.
%Y A347047 These are the minima of rows of A338905.
%Y A347047 The nonsquarefree version is A339114 (opposite: A339115).
%Y A347047 A001358 lists semiprimes (squarefree: A006881).
%Y A347047 A024697 adds up semiprimes by weight (squarefree: A025129).
%Y A347047 A056239 adds up prime indices, row sums of A112798.
%Y A347047 A246868 gives the greatest squarefree number whose prime indices sum to n.
%Y A347047 A320655 counts factorizations into semiprimes (squarefree: A320656).
%Y A347047 A338898, A338912, A338913 give the prime indices of semiprimes.
%Y A347047 A338899, A270650, A270652 give the prime indices of squarefree semiprimes.
%Y A347047 A339116 groups squarefree semiprimes by greater factor, sums A339194.
%Y A347047 A339362 adds up prime indices of squarefree semiprimes.
%Y A347047 Cf. A001221, A087112, A089994, A098350, A176504, A338900, A338901, A338904, A338907/A338908, A339005, A339191.
%K A347047 nonn
%O A347047 3,1
%A A347047 _Gus Wiseman_, Aug 22 2021