A394249 - OEIS

%I #51 Jun 26 2026 22:27:45

%S 0,1,1,2,2,3,3,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,6,7,6,7,6,8,7,9,7,8,8,8,

%T 7,9,8,7,8,8,7,9,7,8,8,8,6,9,7,10,9,10,7,9,9,10,10,8,7,11,7,8,9,10,9,

%U 10,7,9,8,11,6,11,7,9,9,9,9,10,7,10,9,9,6,13,10,8,8,10,7,12,9,8,7,7,8,11,6,9,11,11

%N Number of partitions of n into two 7-smooth numbers.

%C The two 7-smooth numbers can be equal.

%e a(7) = 3 because 7 has 3 ways to be written as two 7-smooth numbers: 7 = 6 + 1 = 5 + 2 = 4 + 3 where 1, 2, 3, 4, 5, and 6 are all 7-smooth numbers.

%o (PARI)

%o A086299(n)=m=n; forprime(p=2, 7, while(m%p==0, m=m/p)); return(m==1)

%o A394249(n)=sum(k=1,n/2,A086299(k*(n-k)))

%Y Cf. A002473, A086299, A397452.

%K nonn

%O 1,4

%A _Zhicheng Wei_, Jun 14 2026