A360643 a(n) is the least A000120-perfect number (A175522) whose binary weight (A000120) is n, or 0 if no such number exists.

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

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