A177343 - OEIS

%I #13 Sep 25 2017 15:33:04

%S 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,

%T 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,

%U 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

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

%C Record values for primes up to 10000:

%C     n  p(n) a(n)

%C     1    2   1

%C     5   11   3

%C     9   23   4

%C    20   71  12

%C    39  167  25

%C   132  743  58

%C   236 1487  62

%C   417 2879  71

%C   675 5039 125

%C   867 6719 168

%C 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

%H Franklin T. Adams-Watters, <a href="/A177343/b177343.txt">Table of n, a(n) for n=1..1229 (primes through 10000)</a>

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

%o (PARI) a(n)=sum(k=2,n=prime(n),A039654(k)==n) \\ _M. F. Hasler_, Sep 25 2017

%Y Cf. A039654, A039653, A292112, A292113.

%K nonn

%O 1,5

%A _Franklin T. Adams-Watters_, May 06 2010