A347047 - OEIS

%I #22 Sep 15 2021 00:28:00

%S 6,10,14,21,26,34,38,46,58,62,74,82,86,94,106,118,122,134,142,146,158,

%T 166,178,194,202,206,214,218,226,254,262,274,278,298,302,314,326,334,

%U 346,358,362,382,386,394,398,422,446,454,458,466,478,482,502,514,526

%N Smallest squarefree semiprime whose prime indices sum to n.

%C Compared to A001747, we have 21 instead of 22 and lack 2 and 4.

%C Compared to A100484 (shifted) we have 21 instead of 22 and lack 4.

%C Compared to A161344, we have 21 instead of 22 and lack 4 and 8.

%C Compared to A339114, we have 11 instead of 9 and lack 4.

%C 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 A squarefree semiprime (A006881) is a product of any two distinct prime numbers.

%e The initial terms and their prime indices:

%e     6: {1,2}

%e    10: {1,3}

%e    14: {1,4}

%e    21: {2,4}

%e    26: {1,6}

%e    34: {1,7}

%e    38: {1,8}

%e    46: {1,9}

%t Table[Min@@Select[Table[Times@@Prime/@y,{y,IntegerPartitions[n,{2}]}],SquareFreeQ],{n,3,50}]

%o (Python)

%o from sympy import prime, sieve

%o def a(n):

%o     p = [0] + list(sieve.primerange(1, prime(n)+1))

%o     return min(p[i]*p[n-i] for i in range(1, (n+1)//2))

%o print([a(n) for n in range(3, 58)]) # _Michael S. Branicky_, Sep 05 2021

%Y The opposite version (greatest instead of smallest) is A332765.

%Y These are the minima of rows of A338905.

%Y The nonsquarefree version is A339114 (opposite: A339115).

%Y A001358 lists semiprimes (squarefree: A006881).

%Y A024697 adds up semiprimes by weight (squarefree: A025129).

%Y A056239 adds up prime indices, row sums of A112798.

%Y A246868 gives the greatest squarefree number whose prime indices sum to n.

%Y A320655 counts factorizations into semiprimes (squarefree: A320656).

%Y A338898, A338912, A338913 give the prime indices of semiprimes.

%Y A338899, A270650, A270652 give the prime indices of squarefree semiprimes.

%Y A339116 groups squarefree semiprimes by greater factor, sums A339194.

%Y A339362 adds up prime indices of squarefree semiprimes.

%Y Cf. A001221, A087112, A089994, A098350, A176504, A338900, A338901, A338904, A338907/A338908, A339005, A339191.

%K nonn

%O 3,1

%A _Gus Wiseman_, Aug 22 2021