

A038550


Products of an odd prime and a power of two (sorted).


6



3, 5, 6, 7, 10, 11, 12, 13, 14, 17, 19, 20, 22, 23, 24, 26, 28, 29, 31, 34, 37, 38, 40, 41, 43, 44, 46, 47, 48, 52, 53, 56, 58, 59, 61, 62, 67, 68, 71, 73, 74, 76, 79, 80, 82, 83, 86, 88, 89, 92, 94, 96, 97, 101, 103, 104, 106, 107, 109, 112, 113, 116, 118, 122, 124, 127
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OFFSET

1,1


COMMENTS

Also, numbers that can be expressed as the sum of k>1 consecutive integers in only one way. The numbers have the form sum{i=j..j+k1}{i}, with j and k integers.  Paolo P. Lava and Giorgio Balzarotti, Aug 21 2007. For example, 37 = 18+19; 48 = 15+16+17; 56 = 5+6+7+8+9+10+11.
Numbers that are difference of two triangular numbers in exactly two ways.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
T. Verhoeff, Rectangular and Trapezoidal Arrangements, J. Integer Sequences, Vol. 2, 1999, #99.1.6.


FORMULA

A001227(a(n)) = 2.  Reinhard Zumkeller, May 01 2012
a(n) ~ 0.5 n log n.  Charles R Greathouse IV, Apr 30 2013


MATHEMATICA

Select[Range[127], DivisorSigma[0, Max[Select[Divisors[#], OddQ]]]1==1&] (* Jayanta Basu, Apr 30 2013 *)
fQ[n_] := Module[{p, e}, {p, e} = Transpose[FactorInteger[n]]; (Length[p] == 2 && p[[1]] == 2 && e[[2]] == 1)  (Length[p] == 1 && p[[1]] > 2 && e[[1]] == 1)]; Select[Range[2, 127], fQ] (* T. D. Noe, Apr 30 2013 *)
upto=150; Module[{pmax=PrimePi[upto], tmax=Ceiling[Log[2, upto]]}, Select[ Sort[ Flatten[ Outer[ Times, Prime[ Range[ 2, pmax]], 2^Range[0, tmax]]]], #<=upto&]] (* Harvey P. Dale, Oct 18 2013 *)


PROG

(Haskell)
a038550 n = a038550_list !! (n1)
a038550_list = filter ((== 2) . a001227) [1..]
 Reinhard Zumkeller, May 01 2012
(PARI) is(n)=isprime(n>>valuation(n, 2)) \\ Charles R Greathouse IV, Apr 30 2013


CROSSREFS

Cf. A093641 (subsequence).
Sequence in context: A154663 A028983 A232682 * A204232 A028730 A028747
Adjacent sequences: A038547 A038548 A038549 * A038551 A038552 A038553


KEYWORD

nonn,easy,nice


AUTHOR

Tom Verhoeff (Tom.Verhoeff(AT)acm.org)


EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Zak Seidov, Sep 15 2007


STATUS

approved



