

A038550


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


30



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 positive integers in only one way.  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. (Edited by M. F. Hasler, Aug 29 2020: "positive" was missing here. If nonnegative integers are allowed, none of the triangular numbers 3, 6, 10, ... would be in the corresponding sequence. If negative integers are also allowed, it would only have powers of 2 (A000079) which are the only positive integers not the sum of more than one consecutive positive integers, since any x > 0 is the sum of 1x through x.)
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
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.  JuriStepan Gerasimov, Aug 16 2016
Sum_{n>=1} 1/a(n)^s = (2^s*P(s)  1)/(2^s  1), for s > 1, where P is the prime zeta function.  Amiram Eldar, Dec 19 2020


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 *)
Flatten@Position[PrimeQ[BitShiftRight[#, IntegerExponent[#, 2]]&/@Range[#]], True]&@127 (* Federico Provvedi, Dec 14 2021 *)


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. A001227, A000265, A237593, A279387.
Subsequences: A334101, A335431, A335911.
Subsequence of A093641 and of A336101.
Sequence in context: A232682 A352826 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



