A063737 Numbers n such that sum of digits of n is equal to the sum of the prime factors of n, counted with multiplicity.

2, 3, 4, 5, 7, 27, 378, 576, 588, 648, 729, 2688, 17496, 19683, 49896, 69888, 3796875, 3857868, 4898880, 5878656, 7077888, 8957952, 2499898464, 34998578496, 49997969280, 2928898896840, 7625597484987, 184958866998359685

Offset

1,1

Comments

a(29) > 10^30. - Giovanni Resta, Apr 23 2017

a(29) > 10^50 if it exists. - Bert Dobbelaere, Jun 16 2024

Links

Table of n, a(n) for n=1..28.

Example

27=3*3*3, 2+7=9, 3+3+3=9. 49896 = 2*2*2*3*3*3*3*7*11, 4+9+8+9+6 = 36, 2+2+2+3+3+3+3+7+11 = 36.

Mathematica

g@n_ := Cases[Union@(Times @@ # & /@Select[Flatten[Table[IntegerPartitions[k, All, Prime@Range@PrimePi@(9*n)], {k, 1, 9*n}], 1], Plus@@#==DigitSum@(Times @@ #) &]),
_?(#<10^n&)];
g@18 (*Requires Mathematica version 14 or later*) (* Hans Rudolf Widmer, Jan 20 2024 *)

Prog

(ARIBAS): var stk: stack; end; for n := 1 to 2000000 do s := itoa(n); for j := 0 to length(s) - 1 do stack_push(stk, atoi(s[j..j])); end; if sum(stack2array(stk)) = sum(factorlist(n)) then write(n, " "); end; end; .
(PARI) isok(m) = my(f=factor(m)); sumdigits(m) == f[, 1]~*f[, 2]; \\ Michel Marcus, Dec 18 2020
(Python) MAXDIGITS=20
maxsum, maxval = 9*MAXDIGITS, 10**MAXDIGITS-1
from sympy import primerange
primes=list(primerange(0, maxsum))
nprimes, results = len(primes), []
def lensumdigits(x):
    s, t = str(x), 0
    for c in s: t+= ord(c)-48
    return len(s), t
def solve(startidx, sump, val):
    for idx in range(startidx, nprimes):
        p=primes[idx]
        s2, v2 = sump+p, val*p
        ld, sd = lensumdigits(v2)
        if sd==s2: results.append(v2)
        if (s2 > maxsum) or (v2 > maxval) or ((p>10) and (s2 > 9*ld)):
            return
        solve(idx, s2, v2)
solve(0, 0, 1) ; print(sorted(results)) # Bert Dobbelaere, Jun 16 2024

Crossrefs

Cf. A001414, A007953.

Sequence in context: A273932 A270831 A063738 * A338121 A278342 A276522

Adjacent sequences: A063734 A063735 A063736 * A063738 A063739 A063740

Keyword

nonn,base,more

Author

Felice Russo, Aug 13 2001

Extensions

More terms from Klaus Brockhaus, Aug 17 2001

More terms from David Wasserman, Jul 11 2002

Status

approved