Combinatorial Analysis - 27.2 Functions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
27.2.E1	${\displaystyle{\displaystyle n=\prod_{r=1}^{\nu\left(n\right)}p^{a_{r}}_{r}}}$ n = \prod_{r=1}^{\nprimesdiv@{n}}p^{a_{r}}_{r}		n = product((p[r])^(a[r]), r = 1..ifactor(n))	Error	Error	Translation Error	-	-
27.2.E7	${\displaystyle{\displaystyle\phi\left(n\right)=\phi_{0}\left(n\right)}}$ \Eulertotientphi[]@{n} = \Eulertotientphi[0]@{n}		Error	EulerPhi[n] == Sum[If[CoprimeQ[n, m], m^(0), 0], {m, 1, n}]	Missing Macro Error	Failure	-	Failed [3 / 3] Result: 1.0 Test Values: {Rule[n, 1]} Result: 1.0 Test Values: {Rule[n, 2]} ... skip entries to safe data
27.2.E9	${\displaystyle{\displaystyle d\left(n\right)=\sum_{d\mathbin{|}n}1}}$ \ndivisors[]@{n} = \sum_{d\divides n}1		numelems(Divisors(n)) = sum(1, d**n in - infinity)	Error	Translation Error	Missing Macro Error	-	-
27.2.E10	${\displaystyle{\displaystyle\sigma_{\alpha}\left(n\right)=\sum_{d\mathbin{|}n}d^{\alpha}}}$ \sumdivisors{\alpha}@{n} = \sum_{d\divides n}d^{\alpha}		add(divisors(alpha)) = sum((d)^(alpha), d**n in - infinity)	Error	Translation Error	Missing Macro Error	-	-