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A104390 2-Smith numbers. 3
32, 42, 60, 70, 104, 152, 231, 315, 316, 322, 330, 342, 361, 406, 430, 450, 540, 602, 610, 612, 632, 703, 722, 812, 1016, 1027, 1029, 1108, 1162, 1190, 1246, 1261, 1304, 1314, 1316, 1351, 1406, 1470, 1510, 1603, 2013, 2054, 2065, 2070, 2071, 2106, 2114 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

McDaniel, W. L., "The Existence of infinitely Many k-Smith numbers", Fibonacci Quarterly, 25(1987), pp. 76-80.

LINKS

Table of n, a(n) for n=1..47.

S. S. Gupta, Smith Numbers.

EXAMPLE

32 is a 2-Smith number because sum of the digits of its prime factors, i.e., Sp (32) = Sp(2*2*2*2*2)= 2 + 2 + 2 + 2 + 2 = 10, which is equal to twice the digit sum of 32, i.e., 2*S(32) = 2*(3 + 2) = 10.

MATHEMATICA

d[n_]:=IntegerDigits[n]; tr[n_]:=Transpose[FactorInteger[n]]; Select[Range[2120], 2Total[d[#]]==Total[d@tr[#][[1]]*tr[#][[2]], 2]&] (* Jayanta Basu, Jun 04 2013 *)

CROSSREFS

Cf. A006753, A104391.

Sequence in context: A167309 A159007 A114042 * A167528 A229115 A035112

Adjacent sequences:  A104387 A104388 A104389 * A104391 A104392 A104393

KEYWORD

nonn,base,changed

AUTHOR

Eric W. Weisstein, Mar 04 2005 and Shyam Sunder Gupta, Mar 11 2005

STATUS

approved

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Last modified August 27 17:19 EDT 2015. Contains 261095 sequences.