cp's OEIS Frontend

A277317 Numbers k such that A277333(k) is a prime.

%I A277317 #34 Jun 20 2025 14:56:14
%S A277317 3,6,18,30,270,450,630,2310,6750,9450,22050,510510,727650,2668050,
%T A277317 3543750,4961250,25467750,29099070
%N A277317 Numbers k such that A277333(k) is a prime.
%C A277317 Sequence A277316 sorted into ascending order. See comments in that entry.
%C A277317 Terms k present in A277319 for which A260443(A048675(k)) = k. - _David A. Corneth_ and _Antti Karttunen_, Oct 13 2016
%o A277317 (PARI)
%o A277317 \\ Naive program that does not work very far:
%o A277317 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From _Michel Marcus_
%o A277317 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 A277317 A260443(n) = if(n<2, n+1, if(!(n%2), A003961(A260443(n/2)), A260443((n-1)/2) * A260443((n+1)/2)));
%o A277317 A277333(n) = { my(k=A048675(n)); if(A260443(k) == n, k, 0); } ;
%o A277317 isA277317 = n -> isprime(A277333(n));  \\ Naive version, very slow.
%o A277317 A061395(n) =  if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After _M. F. Hasler_'s code for A006530.
%o A277317 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 A277317 i=0; n=0; while(i < 30, n++; if(isA277317(n), i++; write("b277317.txt", i, " ", n)));
%o A277317 (Scheme)
%o A277317 ;; With _Antti Karttunen_'s IntSeq-library)
%o A277317 (define A277317 (MATCHING-POS 1 1 (lambda (n) (= 1 (A010051 (A277333 n))))))
%o A277317 (Scheme)
%o A277317 ;; With _Antti Karttunen_'s IntSeq-library)
%o A277317 ;; Doing search in another order:
%o A277317 (define A277317 (COMPOSE A277319 (MATCHING-POS 1 1 (lambda (n) (= (A260443 (A048675 (A277319 n))) (A277319 n))))))
%Y A277317 Cf. A277316.
%Y A277317 Cf. A000040, A010051, A048675, A260443, A277333.
%Y A277317 Intersection of A260442 and A277319.
%Y A277317 Also, after the initial term, the intersection of A277200 and A277319.
%K A277317 nonn,more
%O A277317 1,1
%A A277317 _Antti Karttunen_, Oct 10 2016