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A174460 Smith numbers of order 2. 9
56, 58, 810, 822, 1075, 1519, 1752, 2145, 2227, 2260, 2483, 2618, 2620, 3078, 3576, 3653, 3962, 4336, 4823, 4974, 5216, 5242, 5386, 5636, 5719, 5762, 5935, 5998, 6220, 6424, 6622, 6845, 7015, 7251, 7339, 7705, 7756, 8460, 9254, 9303, 9355, 10481, 10626, 10659 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Composite numbers a(n) such that the sum of digits^2 equals the sum of digits^2 of its prime factors without the numbers of A176670 that have the same digits as its prime factors (without the zero digit).

It seems as though as the order n approaches infinity, the sequence of n-order Smith numbers approaches A176670. Is there a value of n where the only n-order Smith numbers are members of A176670? - Ely Golden, Dec 07 2016

LINKS

Ely Golden and Donovan Johnson, Table of n, a(n) for n = 1..10000 (terms 1 to 1000 by Donovan Johnson)

Patrick Costello, A new largest Smith number, Fibonacci Quarterly 40(4) (2002), 369-371.

Underwood Dudley, Smith numbers, Mathematics Magazine 67(1) (1994), 62-65.

Ely Golden, Smith number sequence generator optimized for order 2.

S. S. Gupta, Smith Numbers, Mathematical Spectrum 37(1) (2004/5), 27-29.

S. S. Gupta, Smith Numbers.

Eric Weisstein's World of Mathematics, Smith number.

Wikipedia, Smith number.

A. Wilansky, Smith Numbers, Two-Year College Math. J. 13(1) (1982), p. 21.

Amin Witno, Another simple construction of Smith numbers, Missouri J. Math. Sci. 22(2) (2010), 97-101.

Amin Witno, Smith multiples of a class of primes with small digital sum, Thai Journal of Mathematics 14(2) (2016), 491-495.

EXAMPLE

a(2) = 58 = 2*29 is a Smith number of order 2 because 5^2 + 8^2 = 2^2 + 2^2 + 9^2 = 89.

MAPLE

for s from 2 to 10000 do g:=nops(ifactors(s)[2]): qsp:=0: for u from 1 to g do z:=ifactors(s)[2, u][1]: h:=0: while (z>0) do z:=iquo(z, 10, 'r'): h:=h+r^2: end do: h:=h*ifactors(s)[2, u][2]: qsp:=qsp+h: end do: z:=s: qs:=0: while (z>0) do z:=iquo(z, 10, 'r'): qs:=qs+r^2: end do: if (qsp=qs) then print(s): end if: end do:

MATHEMATICA

With[{k = 2}, Select[Range[12000], Function[n, And[Total@ Map[#^k &, IntegerDigits@ n] == Total@ Map[#^k &, Flatten@ IntegerDigits[#]], Not[Sort@ DeleteCases[#, 0] &@ IntegerDigits@ n == Sort@ DeleteCases[#, 0] &@ #]] &@ Flatten@ Map[IntegerDigits@ ConstantArray[#1, #2] & @@ # &, FactorInteger@ n]]]] (* Michael De Vlieger, Dec 10 2016 *)

CROSSREFS

Cf. A006753 (Smith numbers), A176670, A178213, A178193, A178203, A178204.

Sequence in context: A235377 A003897 A031319 * A045001 A116660 A047727

Adjacent sequences:  A174457 A174458 A174459 * A174461 A174462 A174463

KEYWORD

nonn,base

AUTHOR

Paul Weisenhorn, Dec 20 2010

STATUS

approved

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Last modified April 9 12:51 EDT 2020. Contains 333352 sequences. (Running on oeis4.)