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

1,2

Comments

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

Links

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

Example

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.

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 *)

Prog

(PARI) SumD(x)= { local(s=0); while (x>9, s+=x%10; x\=10); return(s + x) }
ProdD(x)= { local(p=1); while (x>9 && p>0, p*=x%10; x\=10); return(p*x) }
{ for (n=1, 1000, a=SumD(n)*ProdD(n); write("b066308.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 09 2010
(PARI) a(n) = my(d = digits(n)); vecsum(d) * prod(k=1, #d, d[k]); \\ Michel Marcus, Feb 24 2017

Crossrefs

Cf. A007953, A007954.

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

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

Sequence in context: A111707 A115300 A085942 * A063462 A098736 A002015

Adjacent sequences: A066305 A066306 A066307 * A066309 A066310 A066311

Keyword

base,easy,nonn

Author

Labos Elemer, Dec 13 2001

Extensions

Edited by Jon E. Schoenfield, Jul 09 2018

Status

approved