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A365264
a(n) is the smallest positive integer k whose number of divisors is larger than that of n.
1
2, 4, 4, 6, 4, 12, 4, 12, 6, 12, 4, 24, 4, 12, 12, 12, 4, 24, 4, 24, 12, 12, 4, 36, 6, 12, 12, 24, 4, 36, 4, 24, 12, 12, 12, 48, 4, 12, 12, 36, 4, 36, 4, 24, 24, 12, 4, 60, 6, 24, 12, 24, 4, 36, 12, 36, 12, 12, 4, 120, 4, 12, 24, 24, 12, 36, 4, 24, 12, 36, 4, 120, 4, 12, 24, 24, 12, 36, 4, 60
OFFSET
1,1
COMMENTS
The distinct values in this sequence together with 1 form A002182.
LINKS
FORMULA
a(n) = Min_{ k >= 1, sigma_0(k) > sigma_0(n) }, n>=1.
A002182(n+1) = a(a(...a(1))...) with n >= 0 iterations.
MATHEMATICA
a365264[n_] := NestWhile[#+1&, 1, DivisorSigma[0, n]>=DivisorSigma[0, #]&]
a365264[{m_, n_}] := Map[a365264, Range[m, n]]
a365264[{1, 80}]
PROG
(PARI) a(n) = my(k=1, nd=numdiv(n)); while(numdiv(k) <= nd, k++); k; \\ Michel Marcus, Aug 29 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Hartmut F. W. Hoft, Aug 29 2023
STATUS
approved