A213671 The odd part of n^2 - n + 2.

1, 1, 1, 7, 11, 1, 11, 29, 37, 23, 7, 67, 79, 23, 53, 121, 137, 77, 43, 191, 211, 29, 127, 277, 301, 163, 11, 379, 407, 109, 233, 497, 529, 281, 149, 631, 667, 11, 371, 781, 821, 431, 113, 947, 991, 259, 541, 1129, 1177, 613, 319, 1327, 1379, 179

Offset: 1

Author

Vladimir Shevelev, Mar 03 2013

Keywords

• nonn
• easy

Comments

The first composite term s of this sequence which is not multiple of a prime term appeared before s is a(245) = 29891 = 71*421 - neither of 71, 421 are terms before a(245). - Peter J. C. Moses, Mar 03 2013

The probability that n points uniformly distributed in (or on) a sphere are in the same hemisphere is (n^2-n+2)/2^n, for which this is the numerator. - Charles R Greathouse IV, Sep 18 2013

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000265, A014206.

Programs

Maple

A213671 := proc(n)
        A000265(n^2-n+2) ;
end proc: # R. J. Mathar, Mar 10 2013

Mathematica

Table[k = n^2 - n + 2; k/2^IntegerExponent[k, 2], {n, 100}] (* T. D. Noe, Mar 16 2013 *)

PARI

a(n)=n=n^2-n+2;n>>valuation(n,2) \\ Charles R Greathouse IV, Sep 18 2013

Formula

a(n) = A000265(n^2-n+2). - R. J. Mathar, Mar 10 2013