



1, 3, 4, 6, 13, 7, 9, 18, 10, 12, 28, 15, 25, 63, 16, 19, 33, 39, 21, 43, 22, 24, 88, 27, 61, 48, 30, 46, 58, 31, 34, 138, 60, 36, 73, 37, 40, 123, 72, 42, 313, 45, 67, 78, 49, 94, 93, 81, 51, 163, 52, 54, 193, 55, 57, 103, 64, 102, 213, 105, 85, 108, 172, 66, 118, 69, 127, 438, 70, 75, 133, 111, 109, 303
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OFFSET

1,2


COMMENTS

Shift the prime factorization of odd numbers one step towards larger primes, add one and divide by two.


LINKS

Table of n, a(n) for n=1..74.


FORMULA

a(n) = A048673((2*n)1) = (1+A003961((2*n)1)) / 2 = (1+A249735(n)) / 2.
a(n) = A032766(A249746(n)).


EXAMPLE

For n = 8, the eighth odd number is 2*8  1 = 15 = 3*5 = prime(2) * prime(3). By adding one to both prime indices, we get prime(3) * prime(4) = 5*7 = 35, and ((35+1)/2 = 18, thus a(8) = 18. Here prime(n) = A000040(n).


PROG

(Scheme, two versions)
(define (A254049 n) (A048673 (+ n n 1)))
(define (A254049 n) (/ (+ 1 (A003961 (+ n n 1))) 2))


CROSSREFS

Cf. A032766 (omitting the initial 0, the same sequence sorted into ascending order).
Also a permutation of A253888.
Cf. A000040, A003961, A048673, A249735, A249746, A254050, A254051, A254053.
Sequence in context: A251483 A009287 A061080 * A280289 A137027 A244409
Adjacent sequences: A254046 A254047 A254048 * A254050 A254051 A254052


KEYWORD

nonn


AUTHOR

Antti Karttunen, Jan 24 2015


STATUS

approved



