A183151 Number of partitions of n minus the number of primes <= n.

1, 1, 1, 3, 4, 8, 11, 18, 26, 38, 51, 72, 95, 129, 170, 225, 290, 378, 482, 619, 784, 994, 1246, 1566, 1949, 2427, 3001, 3709, 4555, 5594, 6831, 8338, 10132, 12299, 14872, 17966, 21625, 26003, 31173, 37326, 44570, 53161, 63247, 75161, 89120, 105544, 124739, 147258, 173510, 204211

Offset: 1

Author

Omar E. Pol, Jan 27 2011

Keywords

• nonn

Comments

This has a visualization when the shell model of partition of A135010 is connected to the geometric model of the divisors of the natural numbers of A000005 which gives the location of the prime numbers for d(n)=2. See the illustrations of initial terms in the entries A000005, A000040, A000041 and A000720.

Crossrefs

Cf. A000040, A000041, A000720, A183050.

Programs

Mathematica

Table[PartitionsP[n] - PrimePi[n], {n, 50}]

Formula

a(n) = A000041(n) - A000720(n) = p(n) - primepi(n).