A051801 -id:A051801 - cp's OEIS frontend

A364136 a(n) is the number of distinct products of nonempty submultisets of the digits of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 2, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 2, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 2, 3, 2

Offset: 0

Ctibor O. Zizka, Jul 10 2023

a(n) <= A000005(A051801(n)). - David A. Corneth, Mar 05 2024

			n = 10: products of digits are {0, 1, 0*1}, distinct products of digits are {0, 1}, thus a(10) = 2.
n = 11: products of digits are {1, 1*1}, distinct product of digits is {1}, thus a(11) = 1.
n = 23: products of digits are {2, 3, 2*3}, distinct products of digits are {2, 3, 6}, thus a(23) = 3.

David A. Corneth, Table of n, a(n) for n = 0..10000

Cf. A000005, A007954, A051801, A055642, A360391.

a(n) = {if(n==0, return(1));
	my(d = vecsort(digits(n)), l = List());
	for(i = 1, #d,
		forvec(x = vector(i, j, [1,#d]),
			c = vecprod(vector(i, j, d[x[j]]));
			listput(l, c)
		,
		2
		)
	);
	#Set(l)
} \\ David A. Corneth, Mar 05 2024

A086356 Fixed point if [nonzero-digit product]-function at initial-value=C[2n,n]=central binomial coefficient is iterated.

Original entry on oeis.org

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

Offset: 1

Labos Elemer, Jul 21 2003

			n=10, C[20,10]=184756, iteration list={184756,7560,210,2},
a(100)=2.

Cf. A051801, A051802, A086353-A086361, A029898, A010888, A038194, A000984.

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

a(n)=A051802[A000984(n)]=fixed-point of A051801[C(2n, n)]

A086357 Fixed point if [nonzero-digit-product]-function at initial-value=A002110(n)=n-th primorial is iterated.

Original entry on oeis.org

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

Offset: 1

Labos Elemer, Jul 21 2003

			n=7, 7th-primorial=510510, iteration list={510510,25,10,1},
a(100)=2.

Cf. A051801, A051802, A086353-A086361, A029898, A010888, A038194, A000984.

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

a(n)=A051802[A002110(n)]=fixed-point of A051801[A002110(n)]

A091788 a(1) = 1, a(2) = 2 and a(n) = product of the nonzero digits of all previous terms.

Original entry on oeis.org

1, 2, 2, 4, 16, 96, 5184, 829440, 1911029760, 13002646487040, 10065920762063093760, 9319918463639717615448883200, 137422208150223932126848386360776224407552000

Offset: 1

Amarnath Murthy, Feb 18 2004

Index entries for Colombian or self numbers and related sequences

Cf. A051801, A230101.

p:=proc(n) local pr,nn,j: pr:=1: nn:=convert(n,base,10): for j from 1 to nops(nn) do if nn[j]>0 then pr:=pr*nn[j] else pr:=pr: fi: od: end: a:=proc(n) if n=1 then 1 elif n=2 then 2 elif n=3 then 2 else a(n-1)*p(a(n-1)) fi end: seq(a(n),n=1..14); # p(n) is the product of the nonzero digits of n # Emeric Deutsch, Apr 15 2005

a(n) = a(n-1)*product of nonzero digits of a(n-1) (n >= 4). - Emeric Deutsch, Apr 15 2005

More terms from Emeric Deutsch, Apr 15 2005

A096291 Sum of digits(product of nonzero digits(n^n)).

Original entry on oeis.org

1, 4, 5, 6, 3, 9, 18, 27, 27, 1, 18, 27, 18, 9, 45, 27, 54, 54, 63, 15, 45, 72, 81, 72, 72, 81, 126, 72, 72, 27, 63, 81, 90, 81, 117, 99, 135, 135, 117, 54, 171, 144, 135, 144, 126, 171, 225, 126, 180, 72, 207, 162, 126, 162, 180, 198, 207, 234, 234, 135, 225, 207, 225, 270

Offset: 1

Jason Earls, Jun 24 2004

Conjecture: a(n) = a(n+1) for infinitely many positive integers. Largest found is n=2577, i.e. sd(pnd(2577^2577)) = sd(pnd(2578^2578)) = 18315.

Cf. A051801, A007953.

A096343 Number of 1's in binary expansion(product of nonzero digits(n^n)).

Original entry on oeis.org

1, 1, 3, 4, 4, 4, 4, 6, 6, 1, 6, 5, 10, 5, 16, 14, 12, 17, 22, 4, 9, 21, 21, 22, 18, 25, 22, 21, 15, 4, 27, 28, 29, 23, 32, 34, 39, 38, 52, 13, 45, 56, 50, 53, 27, 50, 44, 48, 47, 18, 48, 62, 42, 47, 48, 44, 57, 67, 58, 31, 71, 66, 63, 57, 71, 67, 56, 74, 70, 42, 100, 89, 72, 60, 75

Offset: 0

Jason Earls, Jun 29 2004

Conjecture: a(n) = a(n+1) for infinitely many positive integers. Largest found is n=1091, i.e. n1b(pnd(1091^1091)) = n1b(pnd(1092^1092)) = 1892.

Cf. A000120, A051801.

Table[Count[IntegerDigits[Times@@DeleteCases[IntegerDigits[n^n],0],2],1],{n,80}] (* Harvey P. Dale, Mar 08 2017 *)

A108697 Numbers n such that a^r + b^r + c^r + ... is prime, where abc* ... is the prime factorization of n and r is the product of the nonzero digits of n.

Original entry on oeis.org

10, 11, 12, 14, 22, 40, 54, 101, 122, 136, 250, 261, 300, 328, 500, 539, 704, 720, 850, 1001, 1016, 1020, 1110, 1112, 1140, 1210, 1402, 2121, 2211, 2220, 2254, 2400, 3081, 3114, 3311, 4011, 4100, 4180, 4510, 6231, 9093, 10110, 10111, 10112, 10203, 10216

Offset: 1

Jason Earls, Jun 19 2005

Of the terms shown, 9093 generates the largest prime, 3^243+7^243+433^243, which has 641 digits. - David Wasserman, May 22 2008

a(74) = 15273. Of the first 74 terms, a(72) = 14464 generates the largest prime, 7*2^384+113^384, which has 789 digits. - David Wasserman, May 22 2008

			22 is in the sequence because 22 = 2*11 and 2^(2*2) + 11^(2*2) = 14657, a prime.

Cf. A051801, A082813.

A020449 is a subsequence.

More terms from David Wasserman, May 22 2008

cp's OEIS Frontend

A364136 a(n) is the number of distinct products of nonempty submultisets of the digits of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A086356 Fixed point if [nonzero-digit product]-function at initial-value=C[2n,n]=central binomial coefficient is iterated.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

A086357 Fixed point if [nonzero-digit-product]-function at initial-value=A002110(n)=n-th primorial is iterated.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

A091788 a(1) = 1, a(2) = 2 and a(n) = product of the nonzero digits of all previous terms.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Formula

Extensions

A096291 Sum of digits(product of nonzero digits(n^n)).

Views

Author

Keywords

Comments

Crossrefs

A096343 Number of 1's in binary expansion(product of nonzero digits(n^n)).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A108697 Numbers n such that a^r + b^r + c^r + ... is prime, where a*b*c* ... is the prime factorization of n and r is the product of the nonzero digits of n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A108697 Numbers n such that a^r + b^r + c^r + ... is prime, where abc* ... is the prime factorization of n and r is the product of the nonzero digits of n.