A061763 -id:A061763 - cp's OEIS frontend

A061762 a(n) = (sum of digits of n) + (product of digits of n).

0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 6, 13, 20, 27, 34, 41, 48, 55, 62, 69, 7, 15, 23, 31, 39, 47

Offset: 0

Amarnath Murthy, May 20 2001

Fixed points a(m) = m are m = {0, 19, 29, 39, 49, 59, 69, 79, 89, 99}. Is this list complete? - Zak Seidov, Aug 22 2007
The above list of fixed points is complete. If a(m) = m, then m < 10^21 and there are no other fixed points below 10^21. - Chai Wah Wu, Aug 14 2017
All numbers are in this sequence. Proof: One can create a number m whose digital sum is any number p and one can create a number k by concatenating digit "0" to m. Then this number k will be a term. - Metin Sariyar, Oct 29 2019

			a(14) = 1+4 + 1*4 = 9.

S. Parmeswaran, S+P numbers, Mathematics Informatics Quarterly, Vol. 9, No. 3 (Sep 1999), Bulgaria.

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

Cf. A007953, A007954, A061763, A038366, A074871.

See A130858 for the smallest inverse.

[0] cat [&+Intseq(n)+&*Intseq(n): n in [1..80]];// Vincenzo Librandi, Jan 03 2020

read("transforms") :
A061762 := proc(n)
    digsum(n)+A007954(n) ;
end proc: # R. J. Mathar, Aug 13 2012

Table[Plus @@ IntegerDigits[n] + Times @@ IntegerDigits[n], {n, 0, 75}] (* Jayanta Basu, Apr 05 2013 *)

a(n) = if (n==0, 0, my(d=digits(n)); vecsum(d) + vecprod(d)); \\ Michel Marcus, Oct 29 2019, Jan 03 2020

from operator import mul
from functools import reduce
def A061762(n):
    a = [int(d) for d in str(n)]
    return sum(a)+reduce(mul,a) # Chai Wah Wu, Aug 14 2017

a(n) = A007953(n) + A007954(n).

Corrected and extended by Larry Reeves (larryr(AT)acm.org) and Matthew Conroy, May 23 2001

A038366 n is divisible by (product of digits) + (sum of digits).

Original entry on oeis.org

10, 19, 20, 29, 30, 39, 40, 42, 49, 50, 59, 60, 69, 70, 79, 80, 89, 90, 99, 100, 102, 108, 110, 120, 126, 132, 140, 150, 180, 190, 200, 201, 204, 207, 209, 210, 220, 230, 240, 270, 280, 285, 300, 306, 308, 312, 320, 330, 360, 370, 400, 402, 405, 407, 408, 410

Offset: 1

Felice Russo

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A061762, A061763.

Select[Range[410], Divisible[#, Plus @@ (x = IntegerDigits[#]) + Times @@ x] &] (* Jayanta Basu, Jul 14 2013 *)

isok(m) = my(d=digits(m)); (m % (vecprod(d) + vecsum(d))) == 0; \\ Michel Marcus, Oct 29 2019

from math import prod
def ok(n): d = list(map(int, str(n))); return n and n%(sum(d)+prod(d)) == 0
print([k for k in range(411) if ok(k)]) # Michael S. Branicky, Oct 19 2021

A371337 Numbers k>0 such that k = (sum of digits of k^2) + (product of nonzero digits of k^2).

Original entry on oeis.org

127, 1467, 3052, 5860, 653230, 3483702, 43352128, 783820873, 8092385362, 622196951140, 1061882796441600145, 178949702436677222562

Offset: 1

René-Louis Clerc, Mar 19 2024

			1467^2 = 2152089, (2+1+5+2+8+9) + (2*1*5*2*8*9) = 27 + 1440 = 1467.

René-Louis Clerc, Nombres S+P, maxSP, minSP et |P-S|, pp. 1-15, 2024.

Cf. A038364, A061763.

SplusP(k,r) = my(d=select(x->(x>0),digits(k^r))); vecsum(d) + vecprod(d) == k;
        resuSplusP(p,r)=for(k=1,10^p,if(SplusP(k,r) ==1,print1(k,",")))

a(9)-a(12) from Chai Wah Wu, Apr 20 2024

A371338 Numbers k>0 such that k = |(product of nonzero digits of k^2) - (sum of digits of k^2)|.

Original entry on oeis.org

161, 198, 1701, 604755, 629810, 4354506, 100018736, 411505847, 14869757951891, 2239397044538572646, 40766979086355529727820, 6289762487609138872319999999757

Offset: 1

René-Louis Clerc, Mar 19 2024

Most often P-S is strictly positive but to always have an application of N* in N* we prefer to use |P-S| (cf. Clerc).

			1701^2 = 2893401, |(2*8*9*3*4*1) - (2+8+9+3+4+1)| = 1728 - 27 = 1701.

René-Louis Clerc, Nombres S+P, maxSP, minSP et |P-S|, pp. 1-15, 2024.

Cf. A038364, A061763.

SmP(k,r)=my(d=select(x->(x>0),digits(k^r))); abs(vecsum(d)- vecprod(d)) == k;
 resuSmP(p,r)={for(k=1,10^p,if(SmP(k,r)==1, print1(k,";")))}

a(9)-a(12) from Chai Wah Wu, Apr 20 2024

cp's OEIS Frontend

A061762 a(n) = (sum of digits of n) + (product of digits of n).

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Python

Formula

Extensions

A038366 n is divisible by (product of digits) + (sum of digits).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Python

A371337 Numbers k>0 such that k = (sum of digits of k^2) + (product of nonzero digits of k^2).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Extensions

A371338 Numbers k>0 such that k = |(product of nonzero digits of k^2) - (sum of digits of k^2)|.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Extensions