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A309439 Number of prime parts in the partitions of n into 10 parts. 1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 5, 11, 17, 30, 45, 72, 104, 157, 210, 298, 396, 537, 698, 924, 1176, 1521, 1909, 2418, 2991, 3729, 4560, 5610, 6795, 8254, 9906, 11919, 14180, 16908, 19972, 23615, 27706, 32527, 37917, 44227, 51267, 59425, 68525, 79007 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,13

LINKS

Table of n, a(n) for n=0..50.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} (A010051(r) + A010051(q) + A010051(p) + A010051(o) + A010051(m) + A010051(l) + A010051(k) + A010051(j) + A010051(i) + A010051(n-i-j-k-l-m-o-p-q-r)).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(PrimePi[i] - PrimePi[i - 1]) + (PrimePi[j] - PrimePi[j - 1]) + (PrimePi[k] - PrimePi[k - 1]) + (PrimePi[l] - PrimePi[l - 1]) + (PrimePi[m] - PrimePi[m - 1]) + (PrimePi[o] - PrimePi[o - 1]) + (PrimePi[p] - PrimePi[p - 1]) + (PrimePi[q] - PrimePi[q - 1]) + (PrimePi[r] - PrimePi[r - 1]) + (PrimePi[n - i - j - k - l - m - o - p - q - r] - PrimePi[n - i - j - k - l - m - o - p - q - r - 1]), {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 50}]

Table[Count[Flatten[IntegerPartitions[n, {10}]], _?PrimeQ], {n, 0, 50}] (* Harvey P. Dale, Dec 26 2020 *)

CROSSREFS

Cf. A010051, A259201.

Sequence in context: A309436 A309437 A309438 * A108542 A006450 A085918

Adjacent sequences:  A309436 A309437 A309438 * A309440 A309441 A309442

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 03 2019

STATUS

approved

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Last modified April 16 05:26 EDT 2021. Contains 343030 sequences. (Running on oeis4.)