A061428 -id:A061428 - cp's OEIS frontend

A061430 Geometric mean of the digits is an integer: k-digit numbers such that the product of the digits is a number of the form m^k.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 19, 20, 22, 28, 30, 33, 40, 41, 44, 49, 50, 55, 60, 66, 70, 77, 80, 82, 88, 90, 91, 94, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 118, 120, 124, 130, 139, 140, 142, 150, 160, 170, 180, 181, 188, 190, 193

Offset: 1

Amarnath Murthy, May 03 2001

			694 is a term as (6*9*4)^(1/3) = 6 is an integer.

T. D. Noe, Table of n, a(n) for n=1..5000

Cf. A061426, A061427, A061428.

a061430 n = a061430_list !! (n-1)
a061430_list = filter g [0..] where
   g u = round (fromIntegral p ** (1 / fromIntegral k)) ^ k == p where
         (p, k) = h (1, 0) u
         h (p, l) 0 = (p, l)
         h (p, l) v = h (p * r, l + 1) v' where (v', r) = divMod v 10
-- Reinhard Zumkeller, Jan 13 2014

Select[Range[0,200],IntegerQ[GeometricMean[IntegerDigits[#]]]&] (* Harvey P. Dale, Feb 15 2012 *)

More terms from Naohiro Nomoto, May 11 2001

A069518 Geometric mean of digits = 4 and digits are in nondecreasing order.

Original entry on oeis.org

4, 28, 44, 188, 248, 444, 1488, 2288, 2448, 4444, 12888, 14488, 22488, 24448, 44444, 118888, 124888, 144488, 222888, 224488, 244448, 444444, 1148888, 1228888, 1244888, 1444488, 2224888, 2244488, 2444448, 4444444, 11288888, 11448888, 12248888, 12444888

Offset: 1

Amarnath Murthy, Mar 30 2002

No number is obtainable by permuting the digits of other members - only one with ascending order of digits is included.

			1488 is a term but 1848 is not.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A061428, A069512, A069516.

a = {}; b = 4; Do[c = Apply[ Times, IntegerDigits[n]]/b^Floor[ Log[10, n] + 1]; If[c == 1 && Position[a, FromDigits[ Sort[ IntegerDigits[n]]]] == {}, Print[n]; a = Append[a, n]], {n, 1, 10^7}]

from math import prod
from sympy.utilities.iterables import multiset_combinations
def auptod(terms):
  n, digits, alst, powsexps2 = 0, 1, [], [(1, 0), (2, 1), (4, 2), (8, 3)]
  while n < terms:
    target = 4**digits
    mcstr = "".join(str(d)*(digits//max(1, r//2)) for d, r in powsexps2)
    for mc in multiset_combinations(mcstr, digits):
      if prod(map(int, mc)) == target:
        n += 1
        alst.append(int("".join(mc)))
        if n == terms: break
    else: digits += 1
  return alst
print(auptod(34)) # Michael S. Branicky, Apr 28 2021

Edited and extended by Robert G. Wilson v, Apr 01 2002

Name edited and a(31) and beyond from Michael S. Branicky, Apr 28 2021

A285094 Corresponding values of geometric means of digits of numbers from A061430.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 0, 2, 4, 0, 3, 0, 2, 4, 6, 0, 5, 0, 6, 0, 7, 0, 4, 8, 0, 3, 6, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 3, 0, 2, 0, 0, 0, 0, 2, 4, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 4, 0

Offset: 0

Jaroslav Krizek, Apr 14 2017

Jaroslav Krizek, Table of n, a(n) for n = 0..3000

Cf. A061430 (numbers with integer geometric mean of digits in base 10).

Sequences of numbers n such that a(n) = k for k = 0 - 9: A011540 (k = 0), A002275 (k = 1), A061426 (k = 2), A061427 (k = 3), A061428 (k = 4), A002279 (k = 5), A061429 (k = 6), A002281 (k = 7), A002282 (k = 8), A002283 (k = 9).

[0] cat [Floor(&*Intseq(n) ^ (1/#Intseq(n))): n in [1..100000] | IsIntegral(&*Intseq(n) ^ (1/#Intseq(n)))];

cp's OEIS Frontend

A061430 Geometric mean of the digits is an integer: k-digit numbers such that the product of the digits is a number of the form m^k.

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A069518 Geometric mean of digits = 4 and digits are in nondecreasing order.

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A285094 Corresponding values of geometric means of digits of numbers from A061430.

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