A066308 a(n) = (sum of digits of n) * (product of digits of n).

1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 0, 6, 16, 30, 48, 70, 96, 126, 160, 198, 0, 12, 30, 54, 84, 120, 162, 210, 264, 324, 0, 20, 48, 84, 128, 180, 240, 308, 384, 468, 0, 30, 70, 120, 180, 250, 330, 420, 520, 630, 0, 42, 96, 162, 240, 330

Offset: 1

Author

Labos Elemer, Dec 13 2001

Keywords

• base
• easy
• nonn

Comments

a(n) can be greater than, less than, or equal to n; see Example section.

Examples

			For n = 12, a(12) = (1 + 2)*(1*2) = 3*2 = 6 < n;
for n = 19, a(19) = (1 + 9)*(1*9) = 90 > n;
for n = 135, a(135) =(1 + 3 + 5)*(1*3*5) = 135 = n.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007953, A007954.

Cf. A038369 (fixed points), A034710, A061672.

Cf. A049101, A049102, A049103, A049104, A049105, A049106.

Programs

Mathematica

asum[x_] := Apply[Plus, IntegerDigits[x]] apro[x_] := Apply[Times, IntegerDigits[x]] a[n]=asum[n]*apro[n]
sdpd[n_]:=Module[{idn=IntegerDigits[n]},Total[idn]Times@@idn]; Array[ sdpd,70] (* Harvey P. Dale, Dec 31 2011 *)

PARI

a(n) = my(d = digits(n)); vecsum(d) * vecprod(d); \\ Michel Marcus, Feb 24 2017

Extensions

Edited by Jon E. Schoenfield, Jul 09 2018