editing

proposed

(define (A285323 n) (cond ((zero? n) 1) ((or (= 1 (A000120 n)) (> (A000040 (+ 1 (A285099 n))) (A000290 (A000040 (+ 1 (A007814 n)))))) (A000290 (A020639 (A019565 n)))) (else (A014673 (A019565 n)))))

The sequence is completely determined by the positions of two least significant 1-bits of n: After initial zero, if n is a power of two (only one 1-bit present) or if prime(1+A285099(n)) > prime(1+A007814(n))^2, a(n) = prime(1+A007814(n))^2, = A020639(A019565(n))^2, otherwise a(n) = prime(1+A285099(n)) = A014673(A019565(n)).

(define (A285323 n) (cond ((zero? n) 1) ((or (= 1 (A000120 n)) (> (A000040 (+ 1 (A285099 n))) (A000290 (A000040 (+ 1 (A007814 n)))))) (A000290 (A020639 (A019565 n)))) (else (A014673 (A019565 n)))))

Cf. A000040, A007814, A014673, A020639, A019565, A065642, A285099, A285110, A285321, A285327.

The sequence is completely determined by the positions of two least significant 1-bits of n: After initial zero, if n is a power of two (only one 1-bit present) or if prime(1+A285099(n)) > prime(1+A007814(n))^2, a(n) = prime(1+A007814(n))^2, otherwise a(n) = prime(1+A285099(n)).

(Scheme)

(Scheme) (define (A285323 n) (/ (A065642 (A065642 (A019565 n))) (A019565 n)))

(define (A285323 n) (cond ((zero? n) 1) ((or (= 1 (A000120 n)) (> (A000040 (+ 1 (A285099 n))) (A000290 (A000040 (+ 1 (A007814 n)))))) (A000290 (A000040 (+ 1 (A007814 n))))) (else (A000040 (+ 1 (A285099 n))))))

Cf. A000040, A007814, A019565, A065642, A285099, A285110, A285321, A285327.

(PARI)

A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler

A007947(n) = factorback(factorint(n)[, 1]); \\ From Andrew Lelechenko, May 09 2014

A065642(n) = { my(r=A007947(n)); if(1==n, n, n = n+r; while(A007947(n) <> r, n = n+r); n); };

A285323(n) = A065642(A065642(A019565(n))) / A019565(n);

Antti Karttunen, <a href="/A285323/b285323.txt">Table of n, a(n) for n = 0..10000</a>

Cf. A019565, A065642, A285110, A285321, A285327.

After the initial zero, a(0)=1, the third row of array A285321 divided by its first row. After 1, all terms are either primes or squares of primes. See A285110.

Cf. A019565, A065642, A285110, A285321.

allocated for Antti Karttunen

a(n) = A065642(A065642(A019565(n))) / A019565(n).

1, 4, 9, 3, 25, 4, 5, 3, 49, 4, 7, 3, 7, 4, 5, 3, 121, 4, 9, 3, 11, 4, 5, 3, 11, 4, 7, 3, 7, 4, 5, 3, 169, 4, 9, 3, 13, 4, 5, 3, 13, 4, 7, 3, 7, 4, 5, 3, 13, 4, 9, 3, 11, 4, 5, 3, 11, 4, 7, 3, 7, 4, 5, 3, 289, 4, 9, 3, 17, 4, 5, 3, 17, 4, 7, 3, 7, 4, 5, 3, 17, 4, 9, 3, 11, 4, 5, 3, 11, 4, 7, 3, 7, 4, 5, 3, 17, 4, 9, 3, 13, 4, 5, 3, 13, 4, 7, 3, 7, 4, 5, 3

0,2

After the initial zero, the third row of array A285321 divided by its first row.

a(n) = A065642(A065642(A019565(n))) / A019565(n).

(Scheme) (define (A285323 n) (/ (A065642 (A065642 (A019565 n))) (A019565 n)))

Cf. A019565, A065642, A285321.

allocated

nonn

Antti Karttunen, Apr 19 2017

approved

editing

allocated for Antti Karttunen

allocated

approved