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A212662 Numbers n for which n’ = x’ + y’, where x > 0, n = x + y, and n’, x’, y’ are the arithmetic derivatives of n, x, y. 4
3, 6, 9, 12, 15, 18, 21, 24, 25, 27, 30, 33, 36, 39, 42, 45, 48, 50, 51, 54, 55, 57, 60, 63, 66, 69, 72, 75, 78, 81, 82, 84, 85, 87, 90, 93, 95, 96, 99, 100, 102, 105, 108, 110, 111, 114, 116, 117, 120, 121, 123, 125, 126, 129, 132, 135, 138, 141, 144, 145 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..5000

EXAMPLE

n=24, x=8, y=16 and 24=8+16; n’=44, x’=12, y’=32 and 44=12+32.

In more than one way:

n=39, x=4, y=35 and 39=4+35; n’=16, x’=4, y’=12 and 16=4+12;

n=39, x=13, y=26 and 39=13+26; n’=16, x’=1, y’=15 and 16=1+15.

n=255, x=54, y=201 and 255=54+201; n’=151, x’=81, y’=70 and 16=4+12;

n=255, x=85, y=170 and 255=85+170; n’=151, x’=22, y’=129 and 16=1+15;

n=255, x=114, y=141 and 39=13+26; n’=151, x’=101, y’=50 and 16=1+15.

MAPLE

with(numtheory);

A212662:=proc(q)

local a, b, c, i, n, p, pfs;

for n from 1 to q do

  pfs:=ifactors(n)[2]; a:=n*add(op(2, p)/op(1, p), p=pfs);

  for i from 1 to trunc(n/2) do

    pfs:=ifactors(i)[2]; b:=i*add(op(2, p)/op(1, p), p=pfs);

    pfs:=ifactors(n-i)[2]; c:=(n-i)*add(op(2, p)/op(1, p), p=pfs);

    if a=b+c then print(n); break; fi;

  od;

od; end:

A212662(1000);

CROSSREFS

Cf. A003415, A211223-A211225, A212663, A212664.

Sequence in context: A003252 A160943 A160930 * A161351 A328168 A209258

Adjacent sequences:  A212659 A212660 A212661 * A212663 A212664 A212665

KEYWORD

nonn

AUTHOR

Paolo P. Lava, May 23 2012

STATUS

approved

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Last modified January 26 20:11 EST 2020. Contains 331288 sequences. (Running on oeis4.)