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A100657 Composite numbers whose prime factors all have the same digital root. 1
4, 8, 9, 16, 22, 25, 27, 32, 44, 49, 58, 64, 81, 88, 94, 115, 116, 121, 125, 128, 166, 169, 176, 188, 202, 205, 232, 242, 243, 256, 274, 289, 295, 301, 319, 332, 343, 346, 352, 361, 376, 382, 403, 404, 427, 454, 464, 484, 512, 517, 526, 529, 548, 553, 562, 565 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

2005 = 5*401. 5 and 401 have the same digital root 5.

2038 = 2*1019. 2 and 1019 have the same digital root 2.

MATHEMATICA

sdrQ[n_]:=CompositeQ[n]&&Length[Union[1+Mod[#-1, 9]&/@FactorInteger[n][[All, 1]]]]==1; Select[Range[600], sdrQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 11 2019 *)

PROG

(PARI) samedr(n) = { local(j); for(j=1, n, if(issamedr(j), print1(j", ")) ) } issamedr(n) = \Test if all factors of n have the same digital root. { local(f, a, ln, x); f=0; a=ifactor(n); ln=length(a); for(x=1, ln-1, if(droot(a[x])<>droot(a[x+1]), f=1; break)); if(f==0&ln>1, return(1), return(0)) } droot(n) = \The digital root of a number. { local(x); x= n%9; if(x>0, return(x), return(9)) }

CROSSREFS

Sequence in context: A003624 A280387 A243180 * A245080 A212164 A293243

Adjacent sequences:  A100654 A100655 A100656 * A100658 A100659 A100660

KEYWORD

base,easy,nonn,changed

AUTHOR

Cino Hilliard, Jan 02 2005

STATUS

approved

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Last modified January 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)