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A038550 Products of an odd prime and a power of two (sorted). 14
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 (list; graph; refs; listen; history; text; internal format)
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+k-1}{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 !! (n-1)

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

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Last modified May 30 04:46 EDT 2016. Contains 273514 sequences.