A394249 Number of partitions of n into two 7-smooth numbers.

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, 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, 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

Offset

1,4

Comments

The two 7-smooth numbers can be equal.

Links

Table of n, a(n) for n=1..100.

Example

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.

Prog

(PARI)
A086299(n)=m=n; forprime(p=2, 7, while(m%p==0, m=m/p)); return(m==1)
A394249(n)=sum(k=1, n/2, A086299(k*(n-k)))

Crossrefs

Cf. A002473, A086299, A397452.

Sequence in context: A260254 A337853 A282711 * A035100 A303594 A085089

Adjacent sequences: A394246 A394247 A394248 * A394250 A394251 A394252

Keyword

nonn,new

Author

Zhicheng Wei, Jun 14 2026

Status

approved