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A082650
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Number of primes < n of form 1+k*spf(n), where spf(n) is the smallest prime factor of n (A020639).
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1
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0, 0, 0, 1, 0, 2, 0, 3, 1, 3, 0, 4, 0, 5, 2, 5, 0, 6, 0, 7, 3, 7, 0, 8, 1, 8, 3, 8, 0, 9, 0, 10, 4, 10, 2, 10, 0, 11, 5, 11, 0, 12, 0, 13, 6, 13, 0, 14, 2, 14, 6, 14, 0, 15, 3, 15, 6, 15, 0, 16, 0, 17, 7, 17, 4, 17, 0, 18, 8, 18, 0, 19, 0, 20, 9, 20, 3, 20, 0, 21, 10, 21, 0, 22, 5, 22, 10, 22, 0
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OFFSET
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1,6
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LINKS
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FORMULA
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EXAMPLE
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For n=20, spf(20) = 2, and there are 8 primes of form 1+k*2: 1+1*2=3, 1+2*2=5,
1+3*2=7, 1+5*2=11, 1+6*2=13, 1+8*2=17, 1+9*2=19, therefore a(20) = 8.
For n=21, spf(21) = 3, and there are 3 primes of form 1+k*3: 1+2*3=7, 1+4*3=13, 1+6*3=19, therefore a(21) = 3.
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MATHEMATICA
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a[n_] := With[{spfn = FactorInteger[n][[1, 1]]}, Select[Range[n-1], PrimeQ[#] && IntegerQ[(#-1)/spfn]&] // Length];
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PROG
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(PARI)
A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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