A062329 -id:A062329 - cp's OEIS frontend

A062998 Numbers whose sum of digits is less than or equal to its product of digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 99, 123, 124, 125, 126, 127, 128, 129, 132, 133, 134, 135

Offset: 1

Henry Bottomley, Jun 29 2001

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

Cf. A007953, A007954, A034710, A062329, A062996, A062997, A062998, A062999.

Not the same as A037344 (contains 124).

isA062998 := proc(n)
        local dgs,s,p ;
        dgs := convert(n,base,10) ;
        s := add(i,i=dgs) ;
        p := mul(i,i=dgs) ;
        if s <= p then
                true;
        else
                false;
        end if;
end proc:
for n from 2 to 150 do
        if isA062998(n) then
                printf("%d,",n) ;
        end if;
end do:   # R. J. Mathar, Aug 14 2025

Select[Range[100],Total[IntegerDigits[#]]<=Times@@IntegerDigits[#]&] (* Harvey P. Dale, Feb 21 2017 *)

isok(k)={my(d=digits(k)); vecsum(d) <= vecprod(d)} \\ Harry J. Smith, Aug 15 2009

is_A062998(n)={normlp(n=digits(n),1)<=prod(i=1,#n,n[i])} \\ M. F. Hasler, Oct 29 2014

A062996 Numbers whose sum of digits is greater than or equal to its product of digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 30, 31, 40, 41, 50, 51, 60, 61, 70, 71, 80, 81, 90, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 130, 131, 132

Offset: 1

Henry Bottomley, Jun 29 2001

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

Cf. A007953, A007954, A034710, A062329, A062996, A062997, A062998, A062999.

Select[Range[150],Total[IntegerDigits[#]]>=Times@@IntegerDigits[#]&] (* Harvey P. Dale, Sep 27 2023 *)

isok(k)={my(d=digits(k)); vecsum(d) >= vecprod(d)} \\ Harry J. Smith, Aug 15 2009

A070565 n - product of digits of n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 50, 46, 42, 38, 34, 30, 26, 22, 18, 14, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 70, 64, 58

Offset: 0

N. J. A. Sloane, May 07 2002

			a(20) = 20 - 2*0 = 20, a(22) = 22 - 2*2 = 18.

Robert Price, Table of n, a(n) for n = 0..10000

Cf. A007954, A062329.

Table[n - Times @@ IntegerDigits[n], {n, 0, 75}]

for(n=1,100,s=ceil(log(n)/log(10)); print1(n-prod(i=0,s-1,floor(n/10^i*1.)-10*floor(n/10^(i+1)*1.)),", "))

a(n) = if (n==0, 0, n - vecprod(digits(n))); \\ Michel Marcus, Jul 22 2025

More terms from Benoit Cloitre and Robert G. Wilson v, May 09 2002

A062997 Numbers whose sum of digits is strictly greater than its product of digits.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 30, 31, 40, 41, 50, 51, 60, 61, 70, 71, 80, 81, 90, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 130, 131, 140, 141, 150, 151, 160, 161, 170

Offset: 1

Amarnath Murthy, Jun 27 2001

Every multiple of 10 is a term.

			118 is a term as 1 + 1 + 8 = 10, 10 > 8 and 8 = 1 * 1 * 8.

Harry J. Smith, Table of n, a(n) for n = 1..1000
Michael De Vlieger, Log log scatterplot of a(n), n = 1..10^6.

Cf. A007953, A007954, A034710, A062329, A062996, A062998, A062999.

Select[Range[170], (Plus @@ IntegerDigits[ # ]) > (Times @@ IntegerDigits[ # ]) &] (* Alonso del Arte, May 16 2005 *)

isok(k)={my(d=digits(k)); vecsum(d) > vecprod(d)} \\ Harry J. Smith, Aug 15 2009

Extended by Larry Reeves (larryr(AT)acm.org) and Henry Bottomley, Jun 29 2001

A062999 Numbers whose sum of the digits is strictly less than its product of digits.

Original entry on oeis.org

23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 92, 93, 94, 95, 96, 97, 98, 99, 124, 125, 126, 127

Offset: 1

Henry Bottomley, Jun 29 2001

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

Cf. A007953, A007954, A034710, A062329, A062996, A062997, A062998, A062999.

Select[Range[128], (Plus @@ IntegerDigits[ # ]) < (Times @@ IntegerDigits[ # ]) &] (* Alonso del Arte, May 16 2005 *)

isok(k)={my(d=digits(k)); vecsum(d) < vecprod(d)} \\ Harry J. Smith, Aug 15 2009

A070566 "Compact" numbers: see reference for definition.

Original entry on oeis.org

2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 49, 53, 57, 59, 61, 67, 71, 73, 79, 83, 87, 89, 93, 97, 101, 103, 107, 109, 113, 117, 121, 127, 131, 137, 139, 145, 149, 151, 157, 163, 167, 169, 173, 177, 179, 181, 189, 191, 193, 197, 199

Offset: 1

N. J. A. Sloane, Sep 22 2008

nonn

The old entry with this sequence number was a duplicate of A062329.

Ray Chandler, Table of n, a(n) for n = 1..10000
Bhupinder Singh Anand, A Minimal Prime Generating Theorem that suggests the Prime Difference is O(pi(p(n)^(1/2)))
Sean A. Irvine, Java program (github)

Cf. A079603, A145554.

A274126 Numbers with digits larger than 1 sorted by product of digits minus sum of digits, then by size.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 22, 23, 24, 222, 25, 33, 26, 27, 34, 223, 28, 29, 35, 44, 224, 2222, 36, 233, 37, 45, 225, 38, 46, 226, 39, 55, 234, 2223, 47, 227, 333, 56, 48, 228, 235, 244, 2224, 22222, 49, 57, 229, 66, 236, 334, 2233, 58, 67, 245, 2225, 237, 59, 68, 335

Offset: 1

David A. Corneth, Jun 10 2016

Let PS(n) be product of digits of n minus sum of digits of n (=-A062329(n)). Then a(n) is PS(A037344(m)) ordered by PS(n) for values of m such that A037344 has its digits in nondecreasing order. If PS(m) some nonzero term m of A002276 exceed some bound, all positive integers t larger than that term without zeros and ones exceed have a larger value for PS(t).
Prepending -A062329(a(n)) or more ones before a(n) gives terms of A274125.
Permuting digits of A274125 gives A254621. Permutations of digits can be found in A261370. The union of A254621 and A011540 is A062996. The b-file lists terms having PS(n) <= 10^6.

			Suppose we want to order the nondecreasing integers without zeros and ones up to PS(m) = 50. We see that 222222 has PS(222222) = 52, so we only have to check such nondecreasing integers up to 222222. Not all of those must be checked, which is used in the program.
25 is a term. Prepending PS(25) = -A062329(25) = 3 ones before 25 gives 11125, which is a term of A274125. Permuting digits of 11125 gives for example 12511, which is a term of A254621.

David A. Corneth, Table of n, a(n) for n = 1..10696
David A. Corneth, PARI program

Cf. A011540, A037344, A062329, A062996, A254621, A261370, A274125.

PARI
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See program in link "PARI program".
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A062998 Numbers whose sum of digits is less than or equal to its product of digits.

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Maple

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PARI

A062996 Numbers whose sum of digits is greater than or equal to its product of digits.

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Mathematica

PARI

A070565 n - product of digits of n.

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Mathematica

PARI

PARI

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A062997 Numbers whose sum of digits is strictly greater than its product of digits.

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Mathematica

PARI

Extensions

A062999 Numbers whose sum of the digits is strictly less than its product of digits.

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Mathematica

PARI

A070566 "Compact" numbers: see reference for definition.

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A274126 Numbers with digits larger than 1 sorted by product of digits minus sum of digits, then by size.

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PARI