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

1,5

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)

Formula

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

Prog

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

Crossrefs

Cf. A039654, A039653, A292112, A292113.

Sequence in context: A191863 A166866 A370220 * A124036 A182481 A066743

Adjacent sequences: A177340 A177341 A177342 * A177344 A177345 A177346

Keyword

nonn

Author

Franklin T. Adams-Watters, May 06 2010

Status

approved