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A038550 Products of an odd prime and a power of two (sorted). 21
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 the difference of two triangular numbers in exactly two ways.

Numbers with largest odd divisor a prime number. - Juri-Stepan Gerasimov, Aug 16 2016

Numbers n such that the symmetric representation of sigma(n) has two subparts. - Omar E. Pol, Dec 28 2016

Numbers k for which A001222(A000265(k)) = 1. - Antti Karttunen, Jul 09 2020

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. - Juri-Stepan 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 !! (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

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

CROSSREFS

Cf. A001227, A000265, A237593, A279387.

Subsequences: A334101, A335431, A335911.

Subsequence of A093641 and of A336101.

Sequence in context: A028983 A232682 A335657 * 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

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Last modified August 3 13:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)