A034710 -id:A034710 - cp's OEIS frontend

A062045 Positive numbers whose product of digits is 12 times their sum.

666, 1479, 1497, 1568, 1586, 1658, 1685, 1749, 1794, 1856, 1865, 1947, 1974, 2349, 2394, 2439, 2446, 2464, 2493, 2644, 2934, 2943, 3249, 3294, 3345, 3354, 3429, 3435, 3453, 3492, 3534, 3543, 3924, 3942, 4179, 4197, 4239, 4246, 4264, 4293, 4329, 4335, 4353, 4392

Offset: 1

Amarnath Murthy, Jun 28 2001

			2349 belongs to the sequence as (2*3*4*9)/(2+3+4+9) = 216/18 = 12.

Harry J. Smith, Table of n, a(n) for n = 1..500

Subsequence of A061013 and hence A038367 and A052382.

Cf. A011540, A034710, A062034, A062035, A062036, A062382, A062037, A062384, A062040, A062041, A062043.

okQ[n_]:=Module[{idn=IntegerDigits[n]},Times@@idn/Total[idn]==12]
Select[Range[10000],okQ] (* Harvey P. Dale, Nov 25 2010 *)

isok(n) = my(d=digits(n)); vecprod(d)==12*vecsum(d) \\ Mohammed Yaseen, Sep 12 2022

from math import prod
def ok(n): d = list(map(int, str(n))); return prod(d) == 12*sum(d)
print([k for k in range(1, 4400) if ok(k)]) # Michael S. Branicky, Sep 12 2022

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jul 06 2001
More terms from Harvey P. Dale, Nov 25 2010
Offset corrected by Mohammed Yaseen, Sep 12 2022

A062384 Positive numbers whose product of digits is 7 times their sum.

Original entry on oeis.org

279, 297, 357, 375, 537, 573, 729, 735, 753, 792, 927, 972, 1447, 1474, 1744, 4147, 4174, 4417, 4471, 4714, 4741, 7144, 7414, 7441, 11367, 11376, 11637, 11673, 11736, 11763, 12247, 12274, 12427, 12472, 12724, 12742, 13167, 13176, 13617, 13671

Offset: 1

Amarnath Murthy, Jun 27 2001

			1447 belongs to the sequence as (1*4*4*7)/(1+4+4+7) = 112/16 = 7.

Harry J. Smith, Table of n, a(n) for n = 1..500

Cf. A011540, A034710, A062034, A062035, A062036, A062382, A062037, A062040, A062041, A062043, A062045.

isok(n) = my(d=digits(n)); vecprod(d)==7*vecsum(d) \\ Mohammed Yaseen, Sep 09 2022

from math import prod
def ok(n): d = list(map(int, str(n))); return n > 0 and prod(d) == 7*sum(d)
print([k for k in range(14000) if ok(k)]) # Michael S. Branicky, Sep 09 2022

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jul 06 2001

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

Original entry on oeis.org

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

A062329 a(n) = (sum of digits of n) - (product of digits of n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, 3, 1, -1, -3, -5, -7, -9, -11, -13, -15, 4, 1, -2, -5, -8, -11, -14, -17, -20, -23, 5, 1, -3, -7, -11, -15, -19, -23, -27, -31, 6, 1, -4, -9, -14, -19, -24, -29, -34, -39, 7, 1, -5, -11, -17, -23, -29, -35, -41, -47, 8, 1, -6, -13, -20, -27

Offset: 0

Amarnath Murthy, Jun 21 2001

			a(23) = 2 + 3 - 2*3 = -1.
a(49) = -(4*9) + (4 + 9) = -36 + 13 = -23.

Harry J. Smith, Table of n, a(n) for n = 0..1000

Cf. A007953, A007954, A034710, A062996, A062997, A062998, A062999, A070565.

A063543 has a similar graph.

a[n_] := (t = IntegerDigits[n]; Plus @@ t - Times @@ t); Table[ a[n], {n, 0, 75}] (* Robert G. Wilson v *)

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 22 2001

Signed version from Henry Bottomley, Jun 29 2001

A249334 Numbers for which the digital sum contains the same distinct digits as the digital product.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 22, 99, 123, 132, 213, 231, 312, 321, 1124, 1137, 1142, 1173, 1214, 1241, 1317, 1371, 1412, 1421, 1713, 1731, 2114, 2141, 2411, 3117, 3171, 3344, 3434, 3443, 3711, 4112, 4121, 4211, 4334, 4343, 4433, 7113, 7131, 7311, 11125, 11133

Offset: 1

Jaroslav Krizek, Oct 25 2014

Numbers k such that A007953(k) contains the same distinct digits as A007954(k). (But either of the two may contain some digit(s) more than once.)
Supersequence of A034710 (positive numbers for which the sum of digits is equal to the product of digits).
Union of A034710 and A249335.
The sequence is infinite since, e.g., A002275(n) = (10^n-1)/9 is in the sequence for all n = A002275(k), k>=0; and more generally N(k,d) = A002275(n)-1+d with n = (A002275(k)-1)*d+1, k>0 and 0M. F. Hasler, Oct 29 2014

			1137 is a term because 1+1+3+7 = 12 and 1*1*3*7 = 21.
3344 is a term because 3+3+4+4=14 has the same (distinct) digits as 3*3*4*4=144.

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..201 from Jaroslav Krizek).

Cf. A034710, A007953, A007954, A249335.

Cf. A061672.

[0] cat [n: n in [1..10^6] | Set(Intseq(&*Intseq(n))) eq Set(Intseq(&+Intseq(n)))];

Select[Range[0,12000],Union[IntegerDigits[Total[IntegerDigits[#]]]]==Union[IntegerDigits[Times@@IntegerDigits[#]]]&] (* Harvey P. Dale, Aug 17 2025 *)

is_A249334(n)=Set(digits(sumdigits(n)))==Set(digits(prod(i=1,#n=digits(n),n[i]))) \\ M. F. Hasler, Oct 29 2014

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

A066307 Nonprimes whose sum of digits is equal to its product of digits.

Original entry on oeis.org

1, 4, 6, 8, 9, 22, 123, 132, 213, 231, 312, 321, 1124, 1142, 1214, 1241, 1412, 1421, 2114, 4112, 4121, 11125, 11133, 11152, 11215, 11222, 11313, 11331, 11512, 11521, 12115, 12122, 12151, 12212, 12221, 13113, 13131, 13311, 15112, 15211, 21115

Offset: 1

Labos Elemer, Dec 13 2001

			321 = 3*107, 3 + 2 + 1 = 6 = 3*2*1.

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..516 from Harry J. Smith)

Composites and 1 from A034710.

Cf. A034710, A066306.

sdpdQ[n_]:=Module[{idn=IntegerDigits[n]},Total[idn]==Times@@idn]; Module[ {upto=25000, cs},cs=Complement[Range[upto],Prime[Range[PrimePi[upto]]]];Select[cs,sdpdQ]] (* Harvey P. Dale, Oct 14 2014 *)

isok(k) = {if(isprime(k), 0, my(d=digits(k)); vecprod(d) == vecsum(d))} \\ Harry J. Smith, Feb 09 2010

A066308 a(n) = (sum of digits of n) * (product of digits of n).

Original entry on oeis.org

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

Labos Elemer, Dec 13 2001

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

			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.

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

Cf. A007953, A007954.
Cf. A038369 (fixed points), A034710, A061672.
Cf. A049101, A049102, A049103, A049104, A049105, A049106.

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 *)

a(n) = my(d = digits(n)); vecsum(d) * vecprod(d); \\ Michel Marcus, Feb 24 2017

Edited by Jon E. Schoenfield, Jul 09 2018

cp's OEIS Frontend

A062045 Positive numbers whose product of digits is 12 times their sum.

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A062384 Positive numbers whose product of digits is 7 times their sum.

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

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

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A062329 a(n) = (sum of digits of n) - (product of digits of n).

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A249334 Numbers for which the digital sum contains the same distinct digits as the digital product.

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Magma

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

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

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