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A240900 Consider a number of k digits n = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1). Sequence lists the numbers n such that sigma(n) - n = Sum_{i=1..k-1}{phi(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below). 2
11, 13, 17, 19, 23, 29, 1363, 2983, 23389, 101299, 132011, 136363, 144133, 198169, 1076441, 1222423, 1973987, 2185367, 2191463, 2673623, 11491523, 18160663, 127666453, 262001569, 264484657, 2080368463, 2763449953, 20603271407, 28272595783 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..29.

EXAMPLE

If n = 132011, starting from the most significant digit, let us cut the number into the set 1, 13, 132, 1320, 13201. We have:

phi(1) = 1;

phi(13) = 12;

phi(132) = 40;

phi(1320) = 320;

phi(13201) = 12852

and 1 + 12 + 40 + 320 + 12852 = 13225 = sigma(132011) - 132011.

MAPLE

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

for n from 2 to q do a:=0; k:=1; while trunc(n/10^k)>0 do a:=a+phi(trunc(n/10^k)); k:=k+1; od;

if sigma(n)-n=a then print(n); fi; od; end: P(10^9);

CROSSREFS

Cf. A000010, A000203, A240894-A240899, A240901, A240902.

Sequence in context: A038842 A293660 A046117 * A091923 A050719 A217062

Adjacent sequences:  A240897 A240898 A240899 * A240901 A240902 A240903

KEYWORD

nonn,base,more

AUTHOR

Paolo P. Lava, Apr 14 2014

EXTENSIONS

a(15)-a(29) from Giovanni Resta, Apr 15 2014

STATUS

approved

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Last modified April 25 04:12 EDT 2019. Contains 322451 sequences. (Running on oeis4.)