A347127 - OEIS

%I #12 Oct 18 2021 14:01:58

%S 1,5,7,8,11,35,15,11,11,55,23,56,27,75,77,14,35,55,39,88,105,115,47,

%T 77,17,135,15,120,59,385,63,17,161,175,165,88,75,195,189,121,83,525,

%U 87,184,121,235,95,98,23,85,245,216,107,75,253,165,273,295,119,616,123,315,165,20,297,805,135,280,329,825,143,121

%N a(n) = A327251(n) / A003557(n).

%H Antti Karttunen, <a href="/A347127/b347127.txt">Table of n, a(n) for n = 1..20000</a>

%F Multiplicative with a(p^e) = ((p+1)*e + p) for prime p.

%F a(n) = A327251(n) / A003557(n).

%t f[p_, e_] := (p + 1)*e + p; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Aug 24 2021 *)

%o (PARI) A347127(n) = { my(f=factor(n)); prod(i=1, #f~, ((f[i, 1]+1)*f[i, 2] + f[i, 1])); };

%o (PARI)

%o A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1))); \\ After code in A001615

%o A003557(n) = (n/factorback(factorint(n)[, 1]));

%o A327251(n) = sumdiv(n, d, A001615(n/d)*d);

%o A347127(n) = (A327251(n) / A003557(n));

%Y Cf. A001615, A003557, A327251.

%Y Cf. also A048250, A347128, A347129.

%K nonn,mult,look

%O 1,2

%A _Antti Karttunen_, Aug 23 2021