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A277317
Numbers n such that A277333(n) is a prime.
6
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
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.
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
KEYWORD
nonn,more
AUTHOR
Antti Karttunen, Oct 10 2016
STATUS
approved