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A008473 If n = Product (p_j^k_j) then a(n) = Product (p_j + k_j). 7
1, 3, 4, 4, 6, 12, 8, 5, 5, 18, 12, 16, 14, 24, 24, 6, 18, 15, 20, 24, 32, 36, 24, 20, 7, 42, 6, 32, 30, 72, 32, 7, 48, 54, 48, 20, 38, 60, 56, 30, 42, 96, 44, 48, 30, 72, 48, 24, 9, 21, 72, 56, 54, 18, 72, 40, 80, 90, 60, 96, 62, 96, 40, 8, 84, 144, 68, 72, 96, 144, 72, 25, 74, 114 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Coincides with sigma (A000203) for squarefree n. - Franklin T. Adams-Watters, Jan 31 2016

Every positive integer except 2 occurs in this sequence, but none occur infinitely often. For m > 4, there are n > m with a(n) = m. This implies that every integer greater than 4 occurs in the iterated sequence infinitely often. For example, 5 <- 8 <- 125 <- 113^12 <- .... - Franklin T. Adams-Watters, Jan 31 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p^e) = p+e. - David W. Wilson, Aug 01 2001

a(n) = Product_{k=1..A001221(n)} (A027748(n,k) + A124010(n,k)). - Reinhard Zumkeller, Jul 17 2014

a(n)/A007947(n) = A322965(n)/A322966(n). - David S. Metzler, Jan 01 2019

MAPLE

A008473 := proc(n) local e, j; e := ifactors(n)[2]:

mul (e[j][1]+e[j][2], j=1..nops(e)) end:

seq (A008473(n), n=1..80);

# Peter Luschny, Jan 17 2011

MATHEMATICA

Array[Times @@ Total /@ FactorInteger[ # ] &, 80] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Jul 28 2006 *)

PROG

(Haskell)

a008473 n = product $ zipWith (+) (a027748_row n) (a124010_row n)

-- Reinhard Zumkeller, Jul 17 2014

(PARI) a(n)=my(f = factor(n)); for (k=1, #f~, f[k, 1] = f[k, 1] + f[k, 2]; f[k, 2] = 1; ); factorback(f); \\ Michel Marcus, Jan 31 2016

CROSSREFS

Cf. A027748, A124010, A001221, A203908, A000203, A322965, A322966.

Sequence in context: A089640 A086659 A265887 * A326043 A069088 A178450

Adjacent sequences:  A008470 A008471 A008472 * A008474 A008475 A008476

KEYWORD

nonn,mult

AUTHOR

Olivier Gérard

EXTENSIONS

More terms from Joseph Biberstine (jrbibers(AT)indiana.edu), Jul 28 2006

STATUS

approved

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Last modified April 5 23:16 EDT 2020. Contains 333260 sequences. (Running on oeis4.)