A051801 -id:A051801 - cp's OEIS frontend

A062331 a(n) is the product of the sum and the product of the digits of n (0 is not to be considered a factor in the product).

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

Offset: 1

Amarnath Murthy, Jun 21 2001

			a(49) = (4+9)*(4*9) = 13*36 = 458.

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Cf. A007953, A051801.

a:= n-> (l-> add(i, i=l)*mul(`if`(i=0, 1, i), i=l))(convert(n, base, 10)):
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 29 2018

psd[n_]:=Module[{idnx0=Select[IntegerDigits[n],#>0&]},Times@@idnx0  Total[idnx0]]
psd/@Range[90]  (* Harvey P. Dale, Feb 24 2011 *)
Array[Times @@ DeleteCases[#, 0]*Total@ # &@ IntegerDigits[#] &, 65] (* Michael De Vlieger, Jun 29 2018 *)

a(n) = sumdigits(n) * vecprod(select(t->t, digits(n))) \\ Harry J. Smith, Aug 05 2009

More terms from Larry Reeves (larryr(AT)acm.org), Jun 22 2001

A101987 Product of nonzero digits of n-th prime.

Original entry on oeis.org

2, 3, 5, 7, 1, 3, 7, 9, 6, 18, 3, 21, 4, 12, 28, 15, 45, 6, 42, 7, 21, 63, 24, 72, 63, 1, 3, 7, 9, 3, 14, 3, 21, 27, 36, 5, 35, 18, 42, 21, 63, 8, 9, 27, 63, 81, 2, 12, 28, 36, 18, 54, 8, 10, 70, 36, 108, 14, 98, 16, 48, 54, 21, 3, 9, 21, 9, 63, 84, 108, 45, 135, 126, 63, 189, 72, 216

Offset: 1

Zak Seidov, Jan 29 2005

First differs from A053666 in 26th term.

			a(25) = 63 because the 25th prime is 97 and 9 * 7 = 63.
a(26) = 1 because the 26th prime is 101, but we ignore the 0 and thus have 1 * 1 = 1.

Cf. A051801, A053666.

Cf. A038618, A056709.

a:= n-> mul(`if`(i=0, 1, i), i=convert(ithprime(n), base, 10)):
seq(a(n), n=1..77);  # Alois P. Heinz, Mar 11 2022

Table[Times@@ReplaceAll[IntegerDigits[Prime[n]], 0 -> 1], {n, 80}] (* Alonso del Arte, Feb 28 2014 *)

a(n) = vecprod(select(x->(x>1), digits(prime(n)))); \\ Michel Marcus, Mar 11 2022

from math import prod
from sympy import sieve
def A051801(n): return prod(int(d) for d in str(n) if d != '0')
def a(n): return A051801(sieve[n])
print([a(n) for n in range(1, 78)]) # Michael S. Branicky, Mar 11 2022

a(n) = A051801(prime(n)). - Michel Marcus, Mar 11 2022

A230101 a(n) = product of n and all its nonzero digits.

Original entry on oeis.org

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 11, 24, 39, 56, 75, 96, 119, 144, 171, 40, 42, 88, 138, 192, 250, 312, 378, 448, 522, 90, 93, 192, 297, 408, 525, 648, 777, 912, 1053, 160, 164, 336, 516, 704, 900, 1104, 1316, 1536, 1764, 250, 255, 520, 795, 1080, 1375, 1680, 1995, 2320, 2655, 360, 366, 744, 1134, 1536, 1950

Offset: 0

N. J. A. Sloane, Oct 12 2013

			a(15) = 15*1*5=75

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for Colombian or self numbers and related sequences

Cf. A007954, A051801, A098736.

with transforms; [seq(n*digprod0(n), n=0..200)];

Table[n*Times@@Select[IntegerDigits[n],#!=0&],{n,0,70}] (* Harvey P. Dale, May 26 2018 *)

a(n) = n*A051801.

A230102 a(0)=1; thereafter a(n+1) = a(n) + (product of digits of a(n)).

Original entry on oeis.org

1, 2, 4, 8, 16, 22, 26, 38, 62, 74, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102, 102

Offset: 0

N. J. A. Sloane, Oct 12 2013

Never gets above 102.

Cf. A007954, A051801, A063108, A230099, A232485.

a230102 n = a230102_list !! n
a230102_list = iterate a230099 1  -- Reinhard Zumkeller, Oct 13 2013

NestList[#+Times@@IntegerDigits[#]&,1,50] (* Harvey P. Dale, Jul 30 2023 *)

A338882 Product of the nonzero digits of (n written in base 9).

Original entry on oeis.org

1, 1, 2, 3, 4, 5, 6, 7, 8, 1, 1, 2, 3, 4, 5, 6, 7, 8, 2, 2, 4, 6, 8, 10, 12, 14, 16, 3, 3, 6, 9, 12, 15, 18, 21, 24, 4, 4, 8, 12, 16, 20, 24, 28, 32, 5, 5, 10, 15, 20, 25, 30, 35, 40, 6, 6, 12, 18, 24, 30, 36, 42, 48, 7, 7, 14, 21, 28, 35, 42, 49, 56, 8, 8, 16, 24, 32, 40, 48, 56, 64

Offset: 0

Ilya Gutkovskiy, Nov 13 2020

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Product of the nonzero digits of (n written in base k): A000012 (k = 2), A117592 (k = 3), A338854 (k = 4), A338803 (k = 5), A338863 (k = 6), A338880 (k = 7), A338881 (k = 8), this sequence (k = 9), A051801 (k = 10).

Cf. A007095, A309788.

Table[Times @@ DeleteCases[IntegerDigits[n, 9], 0], {n, 0, 80}]
nmax = 80; A[] = 1; Do[A[x] = (1 + x + 2 x^2 + 3 x^3 + 4 x^4 + 5 x^5 + 6 x^6 + 7 x^7 + 8 x^8) A[x^9] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Table[Times@@(IntegerDigits[n,9]/.(0->1)),{n,0,80}] (* Harvey P. Dale, Oct 08 2021 *)

a(n) = vecprod(select(x->x, digits(n, 9))); \\ Michel Marcus, Nov 14 2020

G.f. A(x) satisfies: A(x) = (1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 6*x^6 + 7*x^7 + 8*x^8) * A(x^9).

A352598 a(n) is the product of the squares of the nonzero digits of n.

Original entry on oeis.org

1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 1, 4, 9, 16, 25, 36, 49, 64, 81, 4, 4, 16, 36, 64, 100, 144, 196, 256, 324, 9, 9, 36, 81, 144, 225, 324, 441, 576, 729, 16, 16, 64, 144, 256, 400, 576, 784, 1024, 1296, 25, 25, 100, 225, 400, 625, 900, 1225, 1600, 2025, 36, 36, 144, 324

Offset: 1

Michel Marcus, Mar 22 2022

a(n) = 1 iff n is a term > 0 of A007088. - Bernard Schott, Mar 24 2022

Cf. A007088, A051801, A352172.

a[n_] := (Times @@ Select[IntegerDigits[n], # > 1 &])^2; Array[a, 65] (* Amiram Eldar, Mar 22 2022 *)

a(n) = vecprod(apply(x->x^2, select(x->(x>1), digits(n))));

from math import prod
def a(n): return prod(int(d)**2 for d in str(n) if d != '0')
print([a(n) for n in range(1, 64)]) # Michael S. Branicky, Mar 22 2022

from math import prod
def A352598(n): return prod(map(lambda x:(0, 1, 4, 9, 16, 25, 36, 49, 64, 81)[int(x)],filter(lambda x:x>'1',str(n)))) # Chai Wah Wu, Sep 17 2024

a(n) = A051801(n)^2.

a(10*n) = a(n). - Bernard Schott, Mar 24 2022

A066565 Numbers that when multiplied by the product of their nonzero digits produce a square.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 45, 49, 96, 98, 100, 135, 144, 200, 250, 288, 289, 300, 338, 378, 384, 400, 405, 441, 500, 600, 700, 800, 882, 900, 1444, 1445, 1575, 1715, 1800, 2205, 2209, 2744, 2809, 3703, 4418, 4500, 4900, 5290, 6144, 6912, 6962, 7560, 7623

Offset: 1

Amarnath Murthy, Dec 18 2001

			45 is a member as 45*4*5 = 900 = 30^2; 135 is a member as 135*3*5 = 2025 = 45^2; 200 is a member as 200*2 = 400.

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

Cf. A051801.

isok(k) = issquare( k * vecprod(select(x->(x!=0), digits(k))) )

More terms from Jason Earls, Dec 24 2001

Offset changed from 0 to 1 by Harry J. Smith, Mar 04 2010

A066613 Numbers k such that the product of the nonzero digits of k equals the number of divisors of k.

Original entry on oeis.org

1, 2, 14, 22, 24, 32, 42, 116, 122, 126, 141, 202, 211, 221, 222, 260, 280, 340, 402, 411, 440, 512, 620, 840, 1021, 1041, 1062, 1114, 1118, 1128, 1132, 1141, 1144, 1201, 1202, 1206, 1218, 1222, 1242, 1250, 1314, 1332, 1340, 1380, 1401, 1411, 1602, 1611

Offset: 1

Amarnath Murthy, Dec 24 2001

			24 is a term as there are 8 divisors of 24 = 2*4.

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Cf. A000005, A051801, A074312.

f[n_] := Block[ {a = Sort[ IntegerDigits[n]] }, While[ First[a] == 0, a = Drop[a, 1]]; Return[ Apply[ Times, a]]]; Select[ Range[10^4], f[ # ] == Length[ Divisors[ # ]] & ]
pndQ[n_]:=Times@@Select[IntegerDigits[n],#!=0&]==DivisorSigma[0,n]; Select[Range[2000],pndQ] (* Harvey P. Dale, Oct 25 2016 *)

isok(k) = { vecprod(select(x->(x!=0), digits(k))) == numdiv(k) } \\ Harry J. Smith, Mar 12 2010

Corrected and extended by Jason Earls and Robert G. Wilson v, Dec 26 2001

A067067 a(n) = product of nonzero digits of n! (A000142).

Original entry on oeis.org

1, 1, 2, 6, 8, 2, 14, 20, 24, 2304, 2304, 11664, 1512, 2688, 112896, 508032, 18579456, 87091200, 11854080, 368640, 6967296, 22861440, 542126592, 1872809164800, 40633270272, 559872000, 26873856000, 8561413324800, 178362777600

Offset: 0

Amarnath Murthy, Jan 03 2002

			a(10) = 2304 as 10! = 3628800 and 3*6*2*8*8 = 2304.

Harry J. Smith, Table of n, a(n) for n = 0..200

Cf. A000142, A051801.

f[n_] := Block[{d = Sort[ IntegerDigits[n! ]] }, While[ First[d] == 0, d = Drop[d, 1]]; Return[ Apply[ Times, d]]]; Table[ f[n], {n, 0, 30} ]
Table[Times@@DeleteCases[IntegerDigits[n!],0],{n,0,30}] (* Harvey P. Dale, Jan 11 2016 *)

a(n) = {vecprod(select(x->(x!=0), digits(n!)))} \\ Harry J. Smith, May 03 2010

a(n) = A051801(n!).

More terms from Jason Earls, Harvey P. Dale and Robert G. Wilson v, Jan 04 2002

A086354 Fixed point if (nonzero-digit product)-function at initial value 2^n is iterated.

Original entry on oeis.org

2, 4, 8, 6, 6, 8, 6, 6, 1, 8, 8, 2, 6, 2, 2, 4, 8, 2, 1, 6, 2, 2, 6, 8, 2, 8, 2, 8, 2, 2, 8, 6, 6, 2, 2, 6, 2, 2, 6, 8, 8, 6, 3, 4, 2, 2, 6, 6, 2, 8, 6, 2, 2, 9, 8, 6, 6, 5, 8, 2, 8, 8, 2, 6, 2, 8, 8, 8, 5, 8, 8, 8, 2, 8, 6, 4, 8, 6, 2, 7, 1, 8, 8, 4, 2, 8, 8

Offset: 1

Labos Elemer, Jul 21 2003

			n=20, 2^20=1048576, iteration list={1048576,6720,84,32,6}, so a(20)=6.

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Cf. A051801, A051802, A086353-A086361, A029898, A010888.

A051801 := proc(n) local d,j: d:=convert(n,base,10): return mul(`if`(d[j]=0,1,d[j]), j=1..nops(d)): end: A086354 := proc(n) local m: m:=2^n: while(length(m)>1)do m:=A051801(m): od: return m: end: seq(A086354(n),n=1..100); # Nathaniel Johnston, May 04 2011

prd[x_] := Apply[Times, DeleteCases[IntegerDigits[x], 0]] Table[FixedPoint[prd, 2^w], {w, 1, 128}]

a(n) = A051802(2^n) = fixed point of A051801(2^n).

cp's OEIS Frontend

A062331 a(n) is the product of the sum and the product of the digits of n (0 is not to be considered a factor in the product).

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A101987 Product of nonzero digits of n-th prime.

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A230101 a(n) = product of n and all its nonzero digits.

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A230102 a(0)=1; thereafter a(n+1) = a(n) + (product of digits of a(n)).

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Haskell

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A338882 Product of the nonzero digits of (n written in base 9).

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A352598 a(n) is the product of the squares of the nonzero digits of n.

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Python

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A066565 Numbers that when multiplied by the product of their nonzero digits produce a square.

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A066613 Numbers k such that the product of the nonzero digits of k equals the number of divisors of k.