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A126805 "Class-" (or "class-minus") number of prime(n) according to the Erdős-Selfridge classification of primes. 5
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

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

a := proc(n) option remember; local p, pf, e, res; if isprime(n) then pf := ifactors(n-1)[2]; res := 1; for e from 1 to nops(pf) do p := op(1, op(e, pf)); if p > 3 then res := max(res, a(p)+1); fi; od; RETURN(res); else -1; fi; end: for n from 1 to 180 do printf("%d, ", a(ithprime(n))); end:

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. A005109, A005110, A005111, A005112, A081424, A081425.

Cf. A081640, A081641, A129248, 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 November 21 16:04 EST 2019. Contains 329371 sequences. (Running on oeis4.)