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%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
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