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A166651 Totally multiplicative sequence with a(p) = 2p-1 for prime p. 2
1, 3, 5, 9, 9, 15, 13, 27, 25, 27, 21, 45, 25, 39, 45, 81, 33, 75, 37, 81, 65, 63, 45, 135, 81, 75, 125, 117, 57, 135, 61, 243, 105, 99, 117, 225, 73, 111, 125, 243, 81, 195, 85, 189, 225, 135, 93, 405, 169, 243 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Maximum number of divisors for m^2 when m has exactly n divisors. - Franklin T. Adams-Watters, Jan 08 2016

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p^e) = (2p-1)^e. If n = Product p(k)^e(k) then a(n) = Product (2*p(k)-1)^e(k).

MATHEMATICA

a[1] = 1; a[n_] := (fi = FactorInteger[n];  Times @@ ((2*fi[[All, 1]] - 1)^fi[[All, 2]])); Table[a[n], {n, 1, 100}] (* G. C. Greubel, May 21 2016 *)

PROG

(PARI) a(n) = {my(f = factor(n)); for (i=1, #f~, f[i, 1] = (2*f[i, 1]-1)^f[i, 2]; f[i, 2] = 1; ); factorback(f); } \\ Michel Marcus, Jan 09 2016

CROSSREFS

Cf. A003961, A000005.

Sequence in context: A092996 A141264 A062949 * A081500 A030365 A316520

Adjacent sequences:  A166648 A166649 A166650 * A166652 A166653 A166654

KEYWORD

nonn,mult

AUTHOR

Jaroslav Krizek, Oct 18 2009

STATUS

approved

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Last modified August 8 08:27 EDT 2020. Contains 336293 sequences. (Running on oeis4.)