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A338483
a(n) is the smallest number having n smaller numbers with the same number of divisors.
1
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 122, 123, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187, 194, 201, 202, 203, 205, 206, 209, 213
OFFSET
1,1
COMMENTS
Inspired by A047983.
Are there prime terms greater than 31?
LINKS
FORMULA
A047983(a(n)) = n. - Rémy Sigrist, Dec 06 2020
EXAMPLE
The smallest number having two smaller numbers (2 and 3) with the same number of divisors is 5, so a(2) is 5.
MAPLE
N:= 500: # for terms before the first term > N
T:= map(numtheory:-tau, [$1..N]):
M:= max(T):
V:= Vector(M):
for n from 1 to N do
v:= T[n];
V[v]:= V[v]+1;
if not assigned(R[V[v]]) then R[V[v]]:= n fi
od:
for nn from 1 while assigned(R[nn]) do od:
seq(R[i], i=2..nn-1); # Robert Israel, Oct 30 2020
MATHEMATICA
f[n_]:=With[{tau=DivisorSigma[0, n]}, Length[Select[Range[n-1], DivisorSigma[0, #]==tau&]]]; t=Table[f[n], {n, 1, 300}]; a[n_]:=FirstPosition[t, n]; Rest[a/@Range[0, 65]]//Flatten (* f(n) by Jean-François Alcover at A047983 *)
PROG
(PARI) f(n) = {my(d=numdiv(n)); sum(k=1, n-1, (numdiv(k)==d))} \\ A047983
a(n) = my(k=1); while (f(k)!= n, k++); k; \\ Michel Marcus, Oct 30 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ivan N. Ianakiev, Oct 30 2020
STATUS
approved