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A343068 Multiplicative with a(p^e) = e*a(p-1). 2
1, 1, 1, 2, 2, 1, 1, 3, 2, 2, 2, 2, 2, 1, 2, 4, 4, 2, 2, 4, 1, 2, 2, 3, 4, 2, 3, 2, 2, 2, 2, 5, 2, 4, 2, 4, 4, 2, 2, 6, 6, 1, 1, 4, 4, 2, 2, 4, 2, 4, 4, 4, 4, 3, 4, 3, 2, 2, 2, 4, 4, 2, 2, 6, 4, 2, 2, 8, 2, 2, 2, 6, 6, 4, 4, 4, 2, 2, 2, 8, 4, 6, 6, 2, 8, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
FORMULA
a(2^n) = n*a(2-1) = n.
EXAMPLE
a(2) = a(2-1) = 1; a(3) = a(3-1) = 1.
MAPLE
a:= proc(n) option remember; `if`(n=1, 1,
mul(i[2]*a(i[1]-1), i=ifactors(n)[2]))
end:
seq(a(n), n=1..100); # Alois P. Heinz, Apr 04 2021
MATHEMATICA
a[1] = 1; a[p_, s_]:= a[p, s]=s a[p-1];
a[n_]:=a[n]= Module[{aux = FactorInteger[n]}, Product[a[aux[[i, 1]], aux[[i, 2]]], {i, Length[aux]}]]; Table[a[n], {n, 100}]
PROG
(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = f[k, 2]*a(f[k, 1]-1); f[k, 2] = 1); factorback(f); \\ Michel Marcus, Apr 23 2021
CROSSREFS
Sequence in context: A175062 A139767 A207822 * A057555 A075532 A050176
KEYWORD
nonn,mult
AUTHOR
STATUS
approved

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Last modified March 4 15:47 EST 2024. Contains 370532 sequences. (Running on oeis4.)