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 A305671 Most common value of sigma (A000203) among all composites (A073255) up to composite(n) = A002808(n) inclusive, or 0 if there is a tie. 5
 7, 0, 0, 0, 0, 0, 0, 24, 24, 24, 24, 24, 24, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..78. EXAMPLE In the following table, column A lists the n-th composite and column B lists sigma(A(n)). n | A | B | a(n) --------------------- 1 | 4 | 7 | 7 2 | 6 | 12 | 0 3 | 8 | 15 | 0 4 | 9 | 13 | 0 5 | 10 | 18 | 0 6 | 12 | 28 | 0 7 | 14 | 24 | 0 8 | 15 | 24 | 24 <--- first time a value of sigma occurs twice 9 | 16 | 31 | 24 10 | 18 | 39 | 24 11 | 20 | 42 | 24 12 | 21 | 32 | 24 13 | 22 | 36 | 24 14 | 24 | 60 | 24 15 | 25 | 31 | 0 <--- second time a value of sigma occurs twice 16 | 26 | 42 | 0 17 | 27 | 40 | 0 18 | 28 | 56 | 0 19 | 30 | 72 | 0 20 | 32 | 63 | 0 21 | 33 | 48 | 0 22 | 34 | 54 | 0 23 | 35 | 48 | 0 24 | 36 | 91 | 0 25 | 38 | 60 | 0 26 | 39 | 56 | 0 27 | 40 | 90 | 0 28 | 42 | 96 | 0 29 | 44 | 84 | 0 30 | 45 | 78 | 0 31 | 46 | 72 | 0 32 | 48 | 124 | 0 33 | 49 | 57 | 0 34 | 50 | 93 | 0 35 | 51 | 72 | 72 <--- first time a value of sigma occurs three times 36 | 52 | 98 | 72 37 | 54 | 120 | 72 38 | 55 | 72 | 72 <--- fourth occurrence of the value 72 39 | 56 | 120 | 72 40 | 57 | 80 | 72 41 | 58 | 90 | 72 42 | 60 | 168 | 72 43 | 62 | 96 | 72 44 | 63 | 104 | 72 45 | 64 | 127 | 72 46 | 65 | 84 | 72 47 | 66 | 144 | 72 48 | 68 | 126 | 72 49 | 69 | 96 | 72 50 | 70 | 144 | 72 51 | 72 | 195 | 72 52 | 74 | 114 | 72 53 | 75 | 124 | 72 54 | 76 | 140 | 72 55 | 77 | 96 | 0 <--- another value apart from 72 occurs four times 56 | 78 | 168 | 0 MAPLE N:= 100: # to get a(1)..a(N) cmax:= 3*N: Counts:= Vector(cmax): i:= 0: for n from 4 do if isprime(n) then next fi; i:= i+1; if i > N then break fi; s:= numtheory:-sigma(n); if s > cmax then cmax:= s; Counts(s):= 1; else Counts[s]:= Counts[s]+1; fi; vmax:= max[index](Counts): if max(Counts[1..vmax-1]) = Counts[vmax] or max(Counts[vmax+1..-1])=Counts[vmax] then A[i]:= 0 else A[i]:= vmax fi od: seq(A[i], i=1..N); # Robert Israel, Jun 12 2018 MATHEMATICA Block[{c = Select[Range@ 120, CompositeQ], s}, s = DivisorSigma[1, c]; Array[If[Length@ # == 1, #[[1, 1]], 0] &@ Last@ SplitBy[SortBy[Tally@ Take[s, #], Last], Last] &, Length@ s]] (* Michael De Vlieger, Jun 14 2018 *) PROG (PARI) add_sigma(vec, val) = if(val > #vec, vec=concat(vec, vector(val-#vec))); vec[val]++; vec max_pos(vec) = if(#setintersect(vecsort(vec), vector(#vec, t, vecmax(vec))) > 1, return(0), for(k=1, #vec, if(vec[k]==vecmax(vec), return(k)))) terms(n) = my(sig=[], i=0); forcomposite(c=1, , sig=add_sigma(sig, sigma(c)); print1(max_pos(sig), ", "); i++; if(i==n, break)) terms(100) \\ Print initial 100 terms of the sequence CROSSREFS Cf. A000203, A002808, A073255, A305672, A305673, A305674, A305675, A305676. Sequence in context: A354995 A270032 A340980 * A228633 A106226 A229658 Adjacent sequences: A305668 A305669 A305670 * A305672 A305673 A305674 KEYWORD nonn,look AUTHOR Felix Fröhlich, Jun 08 2018 STATUS approved

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Last modified February 21 22:50 EST 2024. Contains 370239 sequences. (Running on oeis4.)