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A177343 Number of times the n-th prime occurs in A039654. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A287872 A191863 A166866 * A124036 A182481 A066743

Adjacent sequences:  A177340 A177341 A177342 * A177344 A177345 A177346

KEYWORD

nonn

AUTHOR

Franklin T. Adams-Watters, May 06 2010

STATUS

approved

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Last modified October 21 04:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)