A037344 -id:A037344 - 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

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
```
See program in link "PARI program".
```

A387032 Numbers k with digits different from 0 and 1.

Original entry on oeis.org

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, 222

Offset: 1

David A. Corneth, Aug 13 2025

A062998 contains numbers like 123, 124, 125,.. which are not in this sequence. - R. J. Mathar, Aug 14 2025

A037344 contains numbers like 2047 and 4095 which are not in this sequence. - R. J. Mathar, Aug 14 2025

			2 is in the sequence since it does not contain 0 nor 1.
12 is not in the sequence since it has digit 1.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Intersection of A052382 and A052383.

Cf. A037344, A172424.

isA387032 := proc(n)
    local d ;
    for d in convert(n,base,10) do
        if d <=1 then
            return false;
        end if;
    end do:
    true ;
end proc:
A387032 := proc(n)
    option remember ;
    local a;
    if n = 1 then
        2;
    else
        for a from procname(n-1)+1 do
            if isA387032(a) then
                return a;
            end if;
        end do;
    end if;
end proc:
seq(A387032(n),n=1..200) ; # R. J. Mathar, Aug 14 2025

Select[Range[222], Total@ DigitCount[#, 10, {0, 1}] == 0 &] (* Michael De Vlieger, Aug 13 2025 *)

is(n) = if(n <= 0, return(0)); Set(digits(n))[1] >= 2

def ok(n): return {"0","1"} & set(str(n)) == set()
print([k for k in range(223) if ok(k)]) # Michael S. Branicky, Aug 13 2025

def A387032(n):
    m = ((k:=7*n+1).bit_length()-1)//3
    return sum((2+((k-(1<<3*m))//(7<<3*j)&7))*10**j for j in range(m)) # Chai Wah Wu, Aug 13 2025

cp's OEIS Frontend

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

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Maple

Mathematica

PARI

PARI

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A387032 Numbers k with digits different from 0 and 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Python