

A038550


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


17



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 the difference of two triangular numbers in exactly two ways.
Numbers with largest odd divisor a prime number.  JuriStepan Gerasimov, Aug 16 2016
Numbers n such that the symmetric representation of sigma(n) has two subparts.  Omar E. Pol, Dec 28 2016


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
A000265(a(n))) = prime.  JuriStepan Gerasimov, Aug 16 2016


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
(MAGMA) [n: n in [1..130]  NumberOfDivisors(2*n) NumberOfDivisors(n) eq 2]; // JuriStepan Gerasimov, Aug 16 2016


CROSSREFS

Cf. A001227, A093641 (subsequence), A000265, A237593, A279387.
Sequence in context: A154663 A028983 A232682 * A204232 A028730 A028747
Adjacent sequences: A038547 A038548 A038549 * A038551 A038552 A038553


KEYWORD

nonn,easy,nice


AUTHOR

Tom Verhoeff


EXTENSIONS

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


STATUS

approved



