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 A126805 "Class-" (or "class-minus") number of prime(n) according to the Erdős-Selfridge classification of primes. 4
 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 2, 2, 4, 2, 3, 2, 3, 2, 1, 2, 3, 3, 1, 2, 2, 3, 1, 2, 2, 2, 2, 4, 2, 2, 2, 1, 4, 3, 4, 2, 2, 1, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 1, 3, 4, 2, 4, 2, 5, 2, 2, 3, 2, 3, 3, 2, 4, 3, 3, 5, 3, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 1, 2, 2, 2, 2, 4, 3, 4, 3, 1, 2, 4, 3, 3, 2, 3, 2, 2, 5, 3, 3, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS This gives the "class-" number as opposed to the "class+" number. Not to be confused with the "class-number" of quadratic form theory. a(n)=1 if A000040(n) is in A005109, a(n)=2 if A000040(n) is in A005110, a(n)=3 if A000040(n) is in A005111 etc. LINKS T. D. Noe, Table of n, a(n) for n=1..10000 Index entries for sequences related to the Erdos-Selfridge classification FORMULA a(n) = max { a(p)+1 ; prime(p) is > 3 and divides prime(n)-1 } union { 1 } - M. F. Hasler, Apr 16 2007 MAPLE A126805 := proc(n) option remember; local p, pe, a; if isprime(n) then a := 1; for pe in ifactors(n-1)[2] do p := op(1, pe); if p > 3 then a := max(a, procname(p)+1); end if; end do; a ; else -1; end if; end proc: seq(A126805(ithprime(n)), n=1..100) ; MATHEMATICA a [n_] := a[n] = Module[{p, pf, e, res}, If[PrimeQ[n], pf = FactorInteger[n-1]; res = 1; For[e = 1, e <= Length[pf], e++, p = pf[[e, 1]]; If[p > 3, res = Max[res, a[p]+1]]]; Return[res], -1]]; Table[a[Prime[n]], {n, 1, 105}] (* Jean-François Alcover, Dec 13 2013, translated from Maple *) PROG (PARI) A126805(n) = { if( n>0, n=-prime(n)); if(( n=factor(-1-n)[, 1] ) & n[ #n]>3, vecsort( vector( #n, i, A126805(-n[i]) ))[ #n]+1, 1) } \\ M. F. Hasler, Apr 16 2007 CROSSREFS Cf. A056637. Sequence in context: A127832 A107249 A062842 * A288003 A304382 A304717 Adjacent sequences: A126802 A126803 A126804 * A126806 A126807 A126808 KEYWORD easy,nonn AUTHOR R. J. Mathar, Feb 23 2007 STATUS approved

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Last modified July 21 06:08 EDT 2024. Contains 374463 sequences. (Running on oeis4.)