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A167344 Totally multiplicative sequence with a(p) = (p-1)*(p+1) = p^2-1 for prime p. 5
1, 3, 8, 9, 24, 24, 48, 27, 64, 72, 120, 72, 168, 144, 192, 81, 288, 192, 360, 216, 384, 360, 528, 216, 576, 504, 512, 432, 840, 576, 960, 243, 960, 864, 1152, 576, 1368, 1080, 1344, 648, 1680, 1152, 1848, 1080, 1536, 1584, 2208, 648, 2304, 1728 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = ((p-1)*(p+1))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-1)*(p(k)+1))^e(k).
a(n) = A003958(n) * A003959(n).
Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 - 2)) = 1.884261780923861906728291280746835210118330549695678826316037127832097567... - Vaclav Kotesovec, Sep 20 2020
a(n) = A340323(n) * A340368(n). - Antti Karttunen, Jan 31 2021
Sum_{k=1..n} a(k) ~ c * n^3, where c = (1/3) * Product_{p prime} (1 - 1/(p^3 - p^2 + 1)) = 0.2487962948... . - Amiram Eldar, Nov 12 2022
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 1)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 10 2016 *)
PROG
(PARI) a(n) = my(f=factor(n)); for (k=1, #f~, f[k, 1] = f[k, 1]^2-1); factorback(f); \\ Michel Marcus, Jan 31 2021
CROSSREFS
Cf. also A335915.
Sequence in context: A191487 A176205 A099256 * A025615 A297324 A223331
KEYWORD
nonn,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved

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Last modified March 29 09:28 EDT 2024. Contains 371268 sequences. (Running on oeis4.)