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A263940 Numbers such that the product of the sum of their anti-divisors and the sum of the reciprocals of their anti-divisors is an integer. 0
3, 4, 6, 37, 96, 937, 2760, 393216 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A066466 is a subset of this sequence.

The sums are 1, 1, 1, 57, 1, 1457, 385, 1, ...

LINKS

Table of n, a(n) for n=1..8.

EXAMPLE

Anti-divisors of 937 are 2, 3, 5, 15, 25, 75, 125, 375 and 625. Their sum is 1250 while the sum of their reciprocals is 1/2 + 1/3 + 1/5 + 1/15 + 1/25 + 1/75 + 1/125 + 1/375 + 1/625 = 1457/1250. Finally 1250 * 1457/1250 = 1457.

MAPLE

with(numtheory); P:=proc(q) local a, b, k, n;

for n from 3 to q do a:=0; b:=0;

for k from 2 to n-1 do if abs((n mod k)-k/2)<1 then a:=a+k; b:=b+1/k;

fi; od; if type(a*b, integer) then print(n); fi; od; end: P(10^4);

MATHEMATICA

f[n_] := Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]; Select[Range[3, 3000], IntegerQ@ Times[Total@ f@ #, Total[1/f@ #]] &] (* Michael De Vlieger, Nov 11 2015 *)

CROSSREFS

Cf. A066272, A066466, A263928.

Sequence in context: A306493 A019209 A019120 * A256326 A239244 A267943

Adjacent sequences:  A263937 A263938 A263939 * A263941 A263942 A263943

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Oct 30 2015

STATUS

approved

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Last modified August 14 18:13 EDT 2022. Contains 356122 sequences. (Running on oeis4.)