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

3, 6, 18, 30, 270, 450, 630, 2310, 6750, 9450, 22050, 510510, 727650, 2668050, 3543750, 4961250, 25467750, 29099070

Offset

1,1

Comments

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

Terms k present in A277319 for which A260443(A048675(k)) = k. - David A. Corneth and Antti Karttunen, Oct 13 2016

Links

Table of n, a(n) for n=1..18.

Prog

(PARI)
\\ Naive program that does not work very far:
A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ Michel Marcus, Oct 10 2016
A260443(n) = if(n<2, n+1, if(!(n%2), A003961(A260443(n/2)), A260443((n-1)/2) * A260443((n+1)/2)));
A277333(n) = { my(k=A048675(n)); if(A260443(k) == n, k, 0); } ;
isA277317 = n -> isprime(A277333(n));  \\ Naive version, very slow.
A061395(n) =  if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After M. F. Hasler's code for A006530.
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.
i=0; n=0; while(i < 30, n++; if(isA277317(n), i++; write("b277317.txt", i, " ", n)));
(Scheme, with Antti Karttunen's IntSeq-library)
(define A277317 (MATCHING-POS 1 1 (lambda (n) (= 1 (A010051 (A277333 n))))))
;; Doing search in another order:
(define A277317 (COMPOSE A277319 (MATCHING-POS 1 1 (lambda (n) (= (A260443 (A048675 (A277319 n))) (A277319 n))))))

Crossrefs

Cf. A277316.

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

Intersection of A260442 and A277319.

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

Sequence in context: A352786 A117863 A103100 * A277318 A277316 A101726

Adjacent sequences: A277314 A277315 A277316 * A277318 A277319 A277320

Keyword

nonn,more

Author

Antti Karttunen, Oct 10 2016

Status

approved