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A324706 The sum of the tri-unitary divisors of n. 4
1, 3, 4, 5, 6, 12, 8, 15, 10, 18, 12, 20, 14, 24, 24, 17, 18, 30, 20, 30, 32, 36, 24, 60, 26, 42, 40, 40, 30, 72, 32, 33, 48, 54, 48, 50, 38, 60, 56, 90, 42, 96, 44, 60, 60, 72, 48, 68, 50, 78, 72, 70, 54, 120, 72, 120, 80, 90, 60, 120, 62, 96, 80, 85, 84, 144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A divisor d of n is tri-unitary if the greatest common bi-unitary divisor of d and n/d is 1.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000

Graeme L. Cohen, On an integer's infinitary divisors, Mathematics of Computation, Vol. 54, No. 189 (1990), pp. 395-411.

Pentti Haukkanen, On the k-ary convolution of arithmetical functions, The Fibonacci Quarterly, Vol. 38, No. 5 (2000) pp. 440-445.

FORMULA

Multiplicative with a(p^3) = 1 + p + p^2 + p^3, a(p^6) = 1 + p^2 + p^4 + p^6, and a(p^e) = 1 + p^e otherwise.

MATHEMATICA

f[p_, e_] := If[e == 3, (p^4-1)/(p-1), If[e==6, (p^8-1)/(p^2-1), p^e+1]]; a[1]=1; a[n_]:= Times @@ f @@@ FactorInteger[n]; Array[a, 100]

PROG

(PARI) A324706(n) = { my(f = factor(n)); prod(i=1, #f~, if(3==f[i, 2], sigma(f[i, 1]^f[i, 2]), if(6==f[i, 2], ((f[i, 1]^8)-1)/((f[i, 1]^2)-1), 1+(f[i, 1]^f[i, 2])))); }; \\ Antti Karttunen, Mar 12 2019

CROSSREFS

Cf. A000203, A034448, A049417, A188999, A322485, A324707, A324708, A324709.

Sequence in context: A181549 A241405 A322485 * A049417 A188999 A186644

Adjacent sequences:  A324703 A324704 A324705 * A324707 A324708 A324709

KEYWORD

nonn,mult

AUTHOR

Amiram Eldar, Mar 11 2019

STATUS

approved

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Last modified August 26 00:35 EDT 2019. Contains 326324 sequences. (Running on oeis4.)