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 A360643 a(n) is the least A000120-perfect number (A175522) whose binary weight (A000120) is n, or 0 if no such number exists. 0
 2, 0, 25, 169, 841, 95, 247, 943, 767, 5999, 6139, 16123, 30655, 90109, 122847, 245695, 522237, 1572591, 1966015, 3932095, 12582651, 28311519, 33423343, 100663023, 133693435, 402128831, 931135479, 1069547515, 1610612607, 11802771447, 12884901567, 25736249279 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Apparently, the sequence is increasing after n = 6. LINKS Table of n, a(n) for n=1..32. EXAMPLE a(1) = 2 since A000120(2) = 1 and A093653(2)/A000120(2) = 4/2 = 2. a(2) = 0 since there is no number m with binary weight 2 and with A093653(m) = 4. a(3) = 25 since A000120(25) = 3 and A093653(25)/A000120(25) = 6/3 = 2, and 25 is the least number with this property. MATHEMATICA seq[len_, nmax_] := Module[{s = Table[-1, {len}], n = 3, c = 2, bw, dbw}, s[[1]] = 2; While[c < len && n <= nmax, bw = DigitCount[n, 2, 1]; If[bw <= len && s[[bw]] < 0, dbw = DivisorSum[n, DigitCount[#, 2, 1] &]; If[dbw == 2*bw, c++; s[[bw]] = n]]; n += 2]; s]; seq[16, 10^6] PROG (PARI) lista(len, nmax) = {my(s = vector(len, i, -1), n = 3, c = 2, bw, dbw); s[1] = 2; while(c < len && n <= nmax, bw = hammingweight(n); if(bw <= len && s[bw] < 0, dbw = sumdiv(n, d, hammingweight(d)); if(dbw == 2*bw, c++; s[bw] = n)); n += 2); s}; CROSSREFS Cf. A000120, A093653, A175522. Sequence in context: A255162 A359006 A097563 * A158045 A157304 A157305 Adjacent sequences: A360640 A360641 A360642 * A360644 A360645 A360646 KEYWORD nonn,base AUTHOR Amiram Eldar, Feb 15 2023 STATUS approved

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Last modified September 9 03:44 EDT 2024. Contains 375759 sequences. (Running on oeis4.)