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A322035 Let p1 <= p2 <= ... <= pk be the prime factors of n, with repetition; let s = 1/p1 + 1/(p1*p2) + 1/(p1*p2*p3) + ... + 1/(p1*p2*...*pk); a(n) = denominator of s. a(1)=1 by convention. 5
1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 6, 13, 7, 5, 16, 17, 18, 19, 5, 21, 11, 23, 12, 25, 13, 27, 14, 29, 10, 31, 32, 11, 17, 35, 36, 37, 19, 39, 10, 41, 42, 43, 22, 15, 23, 47, 24, 49, 50, 17, 13, 53, 27, 55, 28, 57, 29, 59, 20, 61, 31, 63, 64, 65, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

If n=12 we get the prime factors 2,2,3, and s = 1/2 + 1/4 + 1/12 = 5/6. So a(12) = 6.

The fractions s for n >= 2 are 1/2, 1/3, 3/4, 1/5, 2/3, 1/7, 7/8, 4/9, 3/5, 1/11, 5/6, 1/13, 4/7, 2/5, 15/16, 1/17, 13/18, 1/19, 4/5, 8/21, ...

MAPLE

# This generates the terms starting at n=2:

P:=proc(n) local FM: FM:=ifactors(n)[2]: seq(seq(FM[j][1], k=1..FM[j][2]), j=1..nops(FM)) end: # A027746

f0:=[]; f1:=[]; f2:=[];

for n from 2 to 120 do

a:=0; b:=1; t1:=[P(n)];

for i from 1 to nops(t1) do b:=b/t1[i]; a:=a+b; od;

f0:=[op(f0), a]; f1:=[op(f1), numer(a)]; f2:=[op(f2), denom(a)]; od:

f0;    # s

f1;    # A322034

f2;    # A322035

f2-f1; # A322036

CROSSREFS

Cf. A006022, A027746, A322034, A322036.

A017665/A017666 = sum of reciprocals of all divisors of n.

Sequence in context: A309639 A327393 A217434 * A325943 A295126 A235602

Adjacent sequences:  A322032 A322033 A322034 * A322036 A322037 A322038

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane and David James Sycamore, Nov 28 2018

STATUS

approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)