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A083348 Numbers n such that r(n) = Sum(e/p: n=Product(p^e)) > 1. 6
8, 12, 16, 18, 20, 24, 28, 30, 32, 36, 40, 44, 48, 52, 54, 56, 60, 64, 68, 72, 76, 80, 81, 84, 88, 90, 92, 96, 100, 104, 108, 112, 116, 120, 124, 126, 128, 132, 135, 136, 140, 144, 148, 150, 152, 156, 160, 162, 164, 168, 172, 176, 180, 184, 188, 189, 192, 196, 198 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A083345(a(n)>A083346(a(n)); A083345(A051674(n))=A083346(A051674(n)), A083345(A083347(n)) < A083346(A083347(n)).

Numbers n whose arithmetic derivative (A003415) is greater than n: n' > n. - Paolo P. Lava, Sep 22 2009

A168036(a(n)) > 0. - Reinhard Zumkeller, May 22 2015

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

Numbers n such that n = n mod n', where n' is the arithmetic derivative of n. - Paolo P. Lava, Mar 20 2012

MAPLE

with(numtheory);

A083348:= proc(i)

local a, b, n, p, pfs;

for n from 2 to i do

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

  b:=(n mod a); if n=b then print(b); fi;

od; end:

A083348(1000); # Paolo P. Lava, Mar 20 2012

PROG

(Haskell)

a083348 n = a083348_list !! (n-1)

a083348_list = filter ((> 0) . a168036) [1..]

-- Reinhard Zumkeller, May 22 2015, May 10 2011

CROSSREFS

Cf. A003415, A072873, A051674, A083347.

Cf. A168036; subsequence of A100717.

Sequence in context: A091375 A282671 A192991 * A174261 A063539 A253296

Adjacent sequences:  A083345 A083346 A083347 * A083349 A083350 A083351

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Apr 25 2003

STATUS

approved

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Last modified November 21 22:40 EST 2019. Contains 329383 sequences. (Running on oeis4.)