A277317 - OEIS

%I #29 Oct 26 2016 15:14:44

%S 3,6,18,30,270,450,630,2310,6750,9450,22050,510510,727650,2668050,

%T 3543750,4961250,25467750,29099070

%N Numbers n such that A277333(n) is a prime.

%C Sequence A277316 sorted into ascending order. See comments in that entry.

%C Terms k present in A277319 for which A260443(A048675(k)) = k. - _David A. Corneth_ and _Antti Karttunen_, Oct 13 2016

%o (PARI)

%o \\ Naive program that does not work very far:

%o A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From _Michel Marcus_

%o A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ _Michel Marcus_, Oct 10 2016

%o A260443(n) = if(n<2, n+1, if(!(n%2), A003961(A260443(n/2)), A260443((n-1)/2) * A260443((n+1)/2)));

%o A277333(n) = { my(k=A048675(n)); if(A260443(k) == n, k, 0); } ;

%o isA277317 = n -> isprime(A277333(n));  \\ Naive version, very slow.

%o A061395(n) =  if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After _M. F. Hasler_'s code for A006530.

%o isA277317(n) = { my(k); if(3==n, 1, if(n%2 || (omega(n) < A061395(n)), 0, k = A048675(n); if((A260443(k) == n), isprime(k), 0))); }; \\ Somewhat optimized.

%o i=0; n=0; while(i < 30, n++; if(isA277317(n), i++; write("b277317.txt", i, " ", n)));

%o (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (define A277317 (MATCHING-POS 1 1 (lambda (n) (= 1 (A010051 (A277333 n))))))

%o ;; Doing search in another order:

%o (define A277317 (COMPOSE A277319 (MATCHING-POS 1 1 (lambda (n) (= (A260443 (A048675 (A277319 n))) (A277319 n))))))

%Y Cf. A277316.

%Y Cf. A000040, A010051, A048675, A260443, A277333.

%Y Intersection of A260442 and A277319.

%Y Also, after the initial term, the intersection of A277200 and A277319.

%K nonn,more

%O 1,1

%A _Antti Karttunen_, Oct 10 2016