A161184 Digital roots of highly composite numbers (A002182).

1, 2, 4, 6, 3, 6, 9, 3, 6, 3, 9, 6, 9, 9, 3, 9, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 1

Author

Parthasarathy Nambi, Jun 05 2009

Keywords

• nonn
• easy
• base

Comments

a(n)=9 for n > 17 because for those n, the highly composite number A002182(n) is divisible by 9. - T. D. Noe, Jul 28 2009

Examples

			7560 is a highly composite number whose digital root is 9.
		

Crossrefs

Cf. A002182, A010888, A140645.

Programs

Maple

read("transforms3"): L := BFILETOLIST("b002182.txt") : A007953 := proc(n) add(d,d=convert(n,base,10)) ; end: A010888 := proc(n) local a ; a := A007953(n) ; while a > 9 do a := A007953(a) ; od; a; end: for i from 1 to 200 do printf("%d,", A010888(op(i,L))) ; od: # R. J. Mathar, Jun 15 2009

Formula

a(n) = A010888(A140645(n)). - R. J. Mathar, Jun 15 2009

Extensions

Extended by R. J. Mathar, Jun 15 2009