The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A360723 Numbers that have at least one exponent in their canonical prime factorization that is neither 2 nor of the form 2^k-1, k>=1. 3
 16, 32, 48, 64, 80, 81, 96, 112, 144, 160, 162, 176, 192, 208, 224, 240, 243, 256, 272, 288, 304, 320, 324, 336, 352, 368, 400, 405, 416, 432, 448, 464, 480, 486, 496, 512, 528, 544, 560, 567, 576, 592, 608, 624, 625, 648, 656, 672, 688, 704, 720, 729, 736, 752 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers that have at least one powerful divisor that is not infinitary divisor, i.e., numbers k such that A360721(k) < A005361(k). The complement of this sequence is the sequence of numbers all of whose powerful divisors are also infinitary divisors. The related sequence of numbers all of whose infinitary divisors are powerful is the sequence of squares (A000290). The asymptotic density of this sequence is 1 - Product_{p prime} ((1 - 1/p) * (1 + 1/p^2 + Sum_{i>=1} 1/p^(2^i-1))) = 0.071899867098952952524... . LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 MATHEMATICA q[n_] := AnyTrue[FactorInteger[n][[;; , 2]], # != 2 && # + 1 != 2^IntegerExponent[# + 1, 2] &]; Select[Range[1000], q] PROG (PARI) is(n) = {my(e = factor(n)[, 2]); for(i = 1, #e, if(e[i] != 2 && (e[i]+1)>>valuation(e[i]+1, 2) != 1, return(1))); 0; } CROSSREFS Cf. A000225, A000290, A001694, A005361, A077609, A360721. Sequence in context: A048111 A122614 A046101 * A044856 A217558 A044901 Adjacent sequences: A360720 A360721 A360722 * A360724 A360725 A360726 KEYWORD nonn,easy AUTHOR Amiram Eldar, Feb 18 2023 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 25 12:29 EDT 2024. Contains 372788 sequences. (Running on oeis4.)