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A166643
Totally multiplicative sequence with a(p) = 3*(p+1) for prime p.
2
1, 9, 12, 81, 18, 108, 24, 729, 144, 162, 36, 972, 42, 216, 216, 6561, 54, 1296, 60, 1458, 288, 324, 72, 8748, 324, 378, 1728, 1944, 90, 1944, 96, 59049, 432, 486, 432, 11664, 114, 540, 504, 13122, 126, 2592, 132, 2916, 2592, 648, 144, 78732, 576, 2916
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (3*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)+1)^e(k).
a(n) = A165824(n) * A003959(n) = 3^bigomega(n) * A003959(n) = 3^A001222(n) * A003959(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*3^(PrimeOmega[n]), {n, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (3*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 17 2023 *)
PROG
(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = 3*(f[k, 1]+1)); factorback(f); } \\ Michel Marcus, May 21 2016
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Oct 18 2009
STATUS
approved