A100657 Composite numbers whose prime factors all have the same digital root.

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

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

Cf. A002808, A010888.

Sequence in context: A003624 A280387 A243180 * A372280 A361204 A245080

Adjacent sequences: A100654 A100655 A100656 * A100658 A100659 A100660

Keyword

base,easy,nonn

Author

Cino Hilliard, Jan 02 2005

Status

approved