A177343 Number of times the n-th prime occurs in A039654.

1, 1, 1, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 4, 2, 4, 1, 1, 12, 1, 2, 3, 3, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 3, 1, 1, 25, 1, 4, 2, 10, 1, 1, 1, 1, 3, 5, 1, 4, 10, 1, 7, 1, 8, 3, 2, 1, 1, 1, 4, 2, 5, 1, 1, 1, 1, 1, 1, 1, 18, 1, 1, 1, 10, 2, 1, 1, 1, 6, 1, 16, 4, 2, 2, 3, 1, 1, 1, 3, 11, 1, 2, 1, 18, 1, 2, 1, 1, 1, 3

Offset: 1

Author

Franklin T. Adams-Watters, May 06 2010

Keywords

• nonn

Comments

Record values for primes up to 10000:

n p(n) a(n)

1 2 1

5 11 3

9 23 4

20 71 12

39 167 25

132 743 58

236 1487 62

417 2879 71

675 5039 125

867 6719 168

The function A039653(n) = sigma(n)-1 iterated in A039654 satisfies A039653(n) >= n (with equality iff n is a prime), therefore the prime p cannot appear beyond index p in A039654, and it is sufficient to count how many times p = A039654(n) with n < p, cf. Formula. - M. F. Hasler, Sep 25 2017

Links

• Franklin T. Adams-Watters, Table of n, a(n) for n=1..1229 (primes through 10000)

Crossrefs

Cf. A039654, A039653, A292112, A292113.

Programs

PARI

a(n)=sum(k=2,n=prime(n),A039654(k)==n) \\ M. F. Hasler, Sep 25 2017

Formula

a(n) = 1 + # { k < prime(n) | A039654(k) = prime(n) } . - M. F. Hasler, Sep 25 2017