A304776 A weakening function. a(n) = n / A007947(n)^(A051904(n) - 1) where A007947 is squarefree kernel and A051904 is minimum prime exponent.
1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 12, 13, 14, 15, 2, 17, 18, 19, 20, 21, 22, 23, 24, 5, 26, 3, 28, 29, 30, 31, 2, 33, 34, 35, 6, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 7, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 2, 65, 66, 67, 68, 69, 70, 71, 12, 73, 74, 75, 76, 77, 78, 79, 80, 3, 82, 83
Offset: 1
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..20000
Crossrefs
Programs
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Mathematica
spr[n_]:=Module[{f,m},f=FactorInteger[n];m=Min[Last/@f];n/Times@@First/@f^(m-1)]; Array[spr,100] -
PARI
A007947(n) = factorback(factorint(n)[, 1]); A051904(n) = if((1==n),0,vecmin(factor(n)[, 2])); A304776(n) = (n/(A007947(n)^(A051904(n)-1))); \\ Antti Karttunen, May 19 2022
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PARI
a(n) = if(n == 1, 1, my(f = factor(n), p = f[, 1], e = f[, 2]); n / vecprod(p)^(vecmin(e) - 1)); \\ Amiram Eldar, Sep 12 2024
Formula
a(n) = n / A354090(n). - Antti Karttunen, May 19 2022
Sum_{k=1..n} a(k) ~ n^2 / 2. - Amiram Eldar, Sep 12 2024
Extensions
Data section extended up to a(83) by Antti Karttunen, May 19 2022
Comments