A057147 a(n) = n times sum of digits of n.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 22, 36, 52, 70, 90, 112, 136, 162, 190, 40, 63, 88, 115, 144, 175, 208, 243, 280, 319, 90, 124, 160, 198, 238, 280, 324, 370, 418, 468, 160, 205, 252, 301, 352, 405, 460, 517, 576, 637, 250, 306, 364, 424, 486, 550, 616

Offset: 0

Author

N. J. A. Sloane, Sep 13 2000

Keywords

• nonn
• base
• easy
• look

Comments

A056992(n) = A010888(a(n)). - Reinhard Zumkeller, Mar 19 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• F. B. Diniz, About a new family of sequences, arXiv:1607.06082 [math.GM], 2016.

Crossrefs

Cf. A007953, A003634, A005349, A052489, A052490, A003635, A245788.

Iterations: A047892 (start=2), A047912 (start=3), A047897 (start=5), A047898 (start=6), A047899 (start=7), A047900 (start=8), A047901 (start=9), A047902 (start=11).

Programs

Haskell

a057147 n = a007953 n * n  -- Reinhard Zumkeller, Mar 19 2014

Maple

for n from 0 to 150 do printf(`%d,`,n*add(convert(n, base, 10)[i], i=1..nops(convert(n,base, 10)))) od:

Mathematica

Table[n*Total[IntegerDigits[n]], {n, 0, 100}]

PARI

a(n) = n*sumdigits(n) \\ Franklin T. Adams-Watters, Aug 03 2014

Python

[n*sum([int(d) for d in str(n)]) for n in range(10**5)] # Chai Wah Wu, Aug 05 2014

Formula

a(n) = n*A007953(n). - Michel Marcus, Aug 10 2014

G.f.: x * (d/dx) (1/(1 - x))*Sum_{k>=1} (x^k - x^(10^k+k) - 9*x^(10^k))/(1 - x^(10^k)). - Ilya Gutkovskiy, Mar 27 2018

Extensions

More terms from James Sellers and Larry Reeves (larryr(AT)acm.org), Sep 13 2000