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Smallest number that can be written as the sum of a Sophie Germain prime (A005384) and a practical number (A005153) in exactly n ways.
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%I #14 Sep 22 2015 08:05:25

%S 2,3,6,23,31,35,65,59,95,131,173,233,203,239,257,299,317,323,473,443,

%T 635,563,671,719,809,701,779,839,803,1109,971,1049,1139,1343,1103,

%U 1409,1433,1607,1481,1499,1559,1523,1769,1679,1643,2069,2063,2309,2111,2141

%N Smallest number that can be written as the sum of a Sophie Germain prime (A005384) and a practical number (A005153) in exactly n ways.

%e 23 can be written as the sum of a Sophie Germain prime and a practical number in the following three ways: 3 + 20, 5 + 18, 11 + 12.

%e Since 23 is the smallest number that can be expressed like that in exactly three ways, a(3) = 23.

%o (PARI) \\ First define the function is_a005153(n) as in A005153

%o is_a005384(n) = ispseudoprime(n) && ispseudoprime(2*n+1)

%o count(n) = x=1; y=n-1; i=0; while(y > n/2, if((is_a005153(x) && is_a005384(y)) || (is_a005153(y) && is_a005384(x)), i++); x++; y--); i

%o a(n) = k=2; while(count(k)!=n, k++); k

%Y Cf. A005153, A005384, A209253.

%K nonn

%O 0,1

%A _Felix Fröhlich_, Sep 06 2015