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A213240
Numbers n such that sum of digits of n = sum of digits of n’, where n’ is the arithmetic derivative of n.
2
4, 22, 27, 54, 56, 81, 94, 108, 121, 135, 166, 202, 216, 243, 245, 260, 265, 266, 272, 274, 308, 344, 346, 355, 382, 405, 445, 454, 459, 513, 517, 518, 526, 562, 567, 594, 634, 648, 675, 702, 706, 729, 784, 806, 832, 837, 841, 891, 913, 920, 922, 945, 950, 972
OFFSET
1,1
LINKS
EXAMPLE
n=344 and 3+4+4=11; n’=524 and 5+2+4=11.
MAPLE
with(numtheory);
A213240:=proc(q)
local a, b, d, 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); b:=0;
while a>0 do b:=b+(a mod 10); a:=trunc(a/10); od;
a:=n; d:=0; while a>0 do d:=d+(a mod 10); a:=trunc(a/10); od;
if b=d then print(n); fi;
od; end:
A213240(100000000);
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Jun 07 2012
STATUS
approved