login
A371413
Dedekind psi function applied to the cubefull numbers (A036966).
4
1, 12, 24, 36, 48, 96, 108, 150, 192, 432, 324, 384, 392, 864, 768, 750, 1296, 972, 1728, 1800, 1536, 2592, 1452, 3456, 3888, 3600, 3072, 2916, 2366, 2744, 5184, 4704, 3750, 5400, 6912, 7776, 7200, 6144, 5202, 9000, 10368, 9408, 11664, 8748, 7220, 13824, 15552
OFFSET
1,2
LINKS
FORMULA
a(n) = A001615(A036966(n)).
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/((p^2-1)*p)) = 1.231291... (A065487).
MATHEMATICA
psi[n_] := n * Times @@ (1 + 1/FactorInteger[n][[;; , 1]]); psi[1] = 1; Join[{1}, psi /@ Select[Range[20000], AllTrue[Last /@ FactorInteger[#], #1 > 2 &] &]]
(* or *)
f[n_] := Module[{f = FactorInteger[n], p, e}, If[n == 1, 1, p = f[[;; , 1]]; e = f[[;; , 2]]; If[Min[e] > 2, Times @@ ((p+1) * p^(e-1)), Nothing]]]; Array[f, 20000]
PROG
(PARI) dedpsi(f) = prod(i = 1, #f~, (f[i, 1] + 1) * f[i, 1]^(f[i, 2]-1));
lista(max) = {my(f); print1(1, ", "); for(k = 2, max, f = factor(k); if(vecmin(f[, 2]) > 2, print1(dedpsi(f), ", "))); }
CROSSREFS
Similar sequences: A323332, A371412, A371415.
Sequence in context: A069056 A359434 A358693 * A019550 A117304 A022759
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Mar 22 2024
STATUS
approved