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 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 (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 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 1-x through x.) 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 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 !! (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. 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 EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Zak Seidov, Sep 15 2007 STATUS approved

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Last modified December 3 08:35 EST 2022. Contains 358515 sequences. (Running on oeis4.)