A361923 Number of distinct values obtained when the infinitary totient function (A091732) is applied to the infinitary divisors of n.
1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 4, 4, 2, 2, 4, 2, 2, 4, 4, 2, 4, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 2, 4, 2, 4, 4, 2, 2, 4, 2, 2, 4, 4, 2, 4, 4, 4, 4, 2, 2, 8, 2, 2, 4, 4, 4, 4, 2, 4, 4, 4, 2, 4, 2, 2, 4, 4, 4, 4, 2, 4, 2, 2, 2, 7, 4, 2, 4
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
f[p_, e_] := p^(2^(-1 + Position[Reverse@ IntegerDigits[e, 2], 1])); iphi[1] = 1; iphi[n_] := Times @@ (Flatten@ (f @@@ FactorInteger[n]) - 1); idivs[n_] := Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]; idivs[1] = {1}; a[n_] := Length @ Union[iphi /@ idivs[n]]; Array[a, 100] -
PARI
iphi(n) = {my(f=factor(n), b); prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], f[i, 1]^(2^(#b-k)) - 1, 1)))} isidiv(d, f) = {if (d==1, return (1)); for (k=1, #f~, bne = binary(f[k, 2]); bde = binary(valuation(d, f[k, 1])); if (#bde < #bne, bde = concat(vector(#bne-#bde), bde)); for (j=1, #bne, if (! bne[j] && bde[j], return (0)); ); ); return (1); } idivs(n) = {my(d = divisors(n), f = factor(n), idiv = []); for (k=1, #d, if(isidiv(d[k], f), idiv = concat(idiv, d[k])); ); idiv; } \\ Michel Marcus at A077609 a(n) = {my(d = idivs(n)); #Set(apply(x->iphi(x), d));}
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