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 A345395 Composite numbers whose divisors that are larger than 1 are all digitally balanced numbers in base 2 (A031443). 1
 132061, 138421, 151427, 532393, 545269, 546407, 557983, 559609, 568801, 570709, 573193, 579013, 590687, 595853, 599707, 604873, 610777, 624553, 630293, 635213, 2102767, 2105063, 2109383, 2111339, 2123677, 2128187, 2129081, 2129609, 2143961, 2149753, 2151131, 2151661 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The prime numbers with this property are the digitally balanced primes (A066196). All the terms are odd, since if k is an even digitally balanced number then its divisor k/2 is not digitally balanced (since it has one fewer 0 in its binary expansion). Apparently most of the terms are semiprimes (A001358) with 4 divisors. Terms with 3 divisors, i.e., squares of primes: 145178401 = 12049^2, 155575729 = 12473^2, ... The least term with more than 4 divisors is 8897396239 = 163 * 929 * 58757, with 8 divisors. The least term with 6 divisors is 8923691369 = 41 * 14753^2. LINKS Table of n, a(n) for n=1..32. EXAMPLE 132061 is a term since its divisors that are larger than 1 are {41, 3221, 132061}, and their binary representations are {101001, 110010010101, 100000001111011101}. Each one has an equal number of 0's and 1's. MATHEMATICA balQ[n_] := Module[{d = IntegerDigits[n, 2], m}, EvenQ @ (m = Length @ d) && Count[d, 1] == m/2]; Select[Range[9, 10^6, 2], CompositeQ[#] && AllTrue[Rest@Divisors[#], balQ] &] CROSSREFS Subsequence of A031443. Cf. A066196. Sequence in context: A204760 A178287 A234159 * A161356 A236735 A238233 Adjacent sequences: A345392 A345393 A345394 * A345396 A345397 A345398 KEYWORD nonn,base AUTHOR Amiram Eldar, Jun 17 2021 STATUS approved

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Last modified September 16 23:59 EDT 2024. Contains 375984 sequences. (Running on oeis4.)