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A329614
Smallest prime factor of the number of divisors of A108951(n).
9
1, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2
OFFSET
1,2
COMMENTS
Differs from A071187 for the first time at n=324, where a(324) = 5, while A071187(324) = 3. The positions of the differences are listed at A329613.
FORMULA
a(n) = A071187(A108951(n)).
a(n) = A020639(A329605(n)).
EXAMPLE
324 = 18^2 = 2^2 * 3^4, thus A108951(324) = 2^2 * (2*3)^4 = 2^6 * 3^4 = 5184, which has (6+1)*(4+1) = 7 * 5 = 35 divisors, thus a(324) = A020639(35) = 5.
MATHEMATICA
Array[FactorInteger[DivisorSigma[0, #]][[1, 1]] &@ Apply[Times, Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e > 0 :> {Times @@ Prime@ Range@ PrimePi@ p, e}]] &, 105] (* Michael De Vlieger, Nov 18 2019 *)
PROG
(PARI)
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951
A071187(n) = if(1==n, n, my(f = factor(numdiv(n))); vecmin(f[, 1]));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 17 2019
STATUS
approved