A050252 -id:A050252 - cp's OEIS frontend

A379373 Numbers k such that A050252(k) <= A055642(k).

1, 2, 3, 5, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 105, 106, 107, 109, 111, 112, 113, 115, 118, 119, 121, 122, 123, 125, 127, 128, 129, 131, 133, 134, 135

Offset: 1

Paolo Xausa, Dec 21 2024

Some authors call these numbers "economical numbers" (see links) and refer to A046759 as "frugal numbers", while other authors define "economical numbers" to be A046759.

First differs from A046758 at n = 54, where a(54) = 125 is missing from A046758.

			112 is a term because 112 = (2^4)*7; the total number of digits of (2, 4, 7) = 1 + 1 + 1 <= the number of digits of 112 (3).
125 is a term because 125 = 5^3; the total number of digits of (5, 3) = 1 + 1 <= the number of digits of 125 (3).

Paolo Xausa, Table of n, a(n) for n = 1..10000
Richard G. E. Pinch, Economical numbers, arXiv:math/9802046 [math.NT], 1998.
Giovanni Resta, Economical numbers, Numbers Aplenty, 2013.

Union of A046758 and A046759.
Complement of A046760.
Cf. A050252, A055642.

A379373Q[k_] := Total[IntegerLength[Select[Flatten[FactorInteger[k]], # > 1 &]]] <= IntegerLength[k];
Select[Range[200], A379373Q]

from sympy import factorint
def ok(n): return n > 0 and sum(len(str(p))+(len(str(e)) if e>1 else 0) for p, e in factorint(n).items()) <= len(str(n))
print([k for k in range(136) if ok(k)]) # Michael S. Branicky, Dec 22 2024

A055642 Number of digits in the decimal expansion of n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 0

Henry Bottomley, Jun 06 2000

From Hieronymus Fischer, Jun 08 2012: (Start)
For n > 0 the first differences of A117804.
The total number of digits necessary to write down all the numbers 0, 1, 2, ..., n is A117804(n+1). (End)
Here a(0) = 1, but a different common convention is to consider that the expansion of 0 in any base b > 0 has 0 terms and digits. - M. F. Hasler, Dec 07 2018

			Examples:
999: 1 + floor(log_10(999)) = 1 + floor(2.x) = 1 + 2 = 3 or
      ceiling(log_10(999+1)) = ceiling(log_10(1000)) = ceiling(3) = 3;
1000: 1 + floor(log_10(1000)) = 1 + floor(3) = 1 + 3 = 4 or
      ceiling(log_10(1000+1)) = ceiling(log_10(1001)) = ceiling(3.x) = 4;
1001: 1 + floor(log_10(1001)) = 1 + floor(3.x) = 1 + 3 = 4 or
      ceiling(log_10(1001+1)) = ceiling(log_10(1002)) = ceiling(3.x) = 4;

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Cf. A043537, A178788, A046034, A019546, A054899, A122840, A055640, A055641, A102669-A102685, A117804, A160093, A160094, A196563, A196564, A000120, A000788, A023416, A059015 (for base 2).
Cf. A262190, A262198.
Cf. A007953: sum of digits.

a055642 :: Integer -> Int
a055642 = length . show  -- Reinhard Zumkeller, Feb 19 2012, Apr 26 2011

[ #Intseq(n): n in [0..105] ];   //  Bruno Berselli, Jun 30 2011
(Common Lisp) (defun A055642 (n) (if (zerop n) 1 (floor (log n 10)))) ; James Spahlinger, Oct 13 2012

A055642 := proc(n)
        max(1,ilog10(n)+1) ;
end proc:  # R. J. Mathar, Nov 30 2011

Join[{1}, Array[ Floor[ Log[10, 10# ]] &, 104]] (* Robert G. Wilson v, Jan 04 2006 *)
Join[{1},Table[IntegerLength[n],{n,104}]]
IntegerLength[Range[0,120]] (* Harvey P. Dale, Jul 02 2016 *)

a(n)=#Str(n) \\ M. F. Hasler, Nov 17 2008

A055642(n)=logint(n+!n,10)+1 \\ Increasingly faster than the above, for larger n. (About twice as fast for n ~ 10^7.) - M. F. Hasler, Dec 07 2018

def a(n): return len(str(n))
print([a(n) for n in range(121)]) # Michael S. Branicky, May 10 2022

def A055642(n): # Faster than len(str(n)) from ~ 50 digits on
    L = math.log10(n or 1)
    if L.is_integer() and 10**int(L)>n: return int(L or 1)
    return int(L)+1  # M. F. Hasler, Apr 08 2024

a(A046760(n)) < A050252(A046760(n)); a(A046759(n)) > A050252(A046759(n)). - Reinhard Zumkeller, Jun 21 2011
a(n) = A196563(n) + A196564(n).
a(n) = 1 + floor(log_10(n)) = 1 + A004216(n) = ceiling(log_10(n+1)) = A004218(n+1), if n >= 1. - Daniel Forgues, Mar 27 2014
a(A046758(n)) = A050252(A046758(n)). - Reinhard Zumkeller, Jun 21 2011
a(n) = A117804(n+1) - A117804(n), n > 0. - Hieronymus Fischer, Jun 08 2012
G.f.: g(x) = 1 + (1/(1-x))*Sum_{j>=0} x^(10^j). - Hieronymus Fischer, Jun 08 2012
a(n) = A262190(n) for n < 100; a(A262198(n)) != A262190(A262198(n)). - Reinhard Zumkeller, Sep 14 2015

A046759 Economical numbers: write n as a product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n) < l(n).

Original entry on oeis.org

125, 128, 243, 256, 343, 512, 625, 729, 1024, 1029, 1215, 1250, 1280, 1331, 1369, 1458, 1536, 1681, 1701, 1715, 1792, 1849, 1875, 2048, 2187, 2197, 2209, 2401, 2560, 2809, 3125, 3481, 3584, 3645, 3721, 4096, 4374, 4375, 4489, 4802, 4913

Offset: 1

N. J. A. Sloane, Dec 11 1999

A050252(a(n)) < A055642(a(n)). - Reinhard Zumkeller, Jun 21 2011

			125 = 5^3, l(n) = 3 and D(n) = 2, so 125 is a member of the sequence.

Bernardo Recamán, The Bogota Puzzles, Courier Dover Publications, Inc., 2020, p. 77.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
C. K. Caldwell, The Prime Glossary, economical number.
J.-M. De Koninck and F. Luca, On strings of consecutive economical numbers of arbitrary length, INTEGERS (2005), Volume: 5, Issue: 2, #A5.
Jean-Paul Delahaye, Les chasseurs de nombres premiers, Pour la Science, No. 258 April 1999. [v1].
R. G. E. Pinch, Economical numbers.
R. G. E. Pinch, Economical numbers, arXiv:math/9802046 [math.NT], 1998.
W. Schneider, Economical Numbers.
G. Villemin's Almanach of Numbers, Nombres Economes.
Eric Weisstein's World of Mathematics, Economical Number.
Wikipedia, Frugal number.

Cf. A046758, A046760.

a046759 n = a046759_list !! (n-1)
a046759_list = filter (\n -> a050252 n < a055642 n) [1..]
-- Reinhard Zumkeller, Jun 21 2011

ecoQ[n_] := Total[ Length /@ IntegerDigits /@ Flatten[ FactorInteger[n] /. {p_, 1} -> p]] < Length[ IntegerDigits[n]]; Select[ Range[5000], ecoQ] (* Jean-François Alcover, Jul 28 2011 *)

is(n)=my(f=factor(n));sum(i=1,#f[,1], #Str(f[i,1])+if(f[i,2]>1, #Str(f[i,2])))<#Str(n) && n>1 \\ Charles R Greathouse IV, Feb 01 2013

from sympy import factorint
def ok(n): return n > 1 and sum(len(str(p))+(len(str(e)) if e>1 else 0) for p, e in factorint(n).items()) < len(str(n))
print([k for k in range(5000) if ok(k)]) # Michael S. Branicky, Dec 22 2024

More terms from Eric W. Weisstein

A046758 Equidigital numbers.

Original entry on oeis.org

1, 2, 3, 5, 7, 10, 11, 13, 14, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 35, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 105, 106, 107, 109, 111, 112, 113, 115, 118, 119, 121, 122, 123, 127, 129, 131, 133, 134, 135, 137, 139

Offset: 1

N. J. A. Sloane

Write n as product of primes raised to powers, let D(n) = A050252 = total number of digits in product representation (number of digits in all the primes plus number of digits in all the exponents that are greater than 1) and l(n) = number of digits in n; sequence gives n such that D(n)=l(n).

The term "equidigital number" was coined by Recamán (1995). - Amiram Eldar, Mar 10 2024

			For n = 125 = 5^3, l(n) = 3 but D(n) = 2. So 125 is not a member of this sequence.

Bernardo Recamán Santos, Equidigital representation: problem 2204, J. Rec. Math., Vol. 27, No. 1 (1995), pp. 58-59.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
J. P. Delahaye, "Primes Hunters", Economical and Prodigal Numbers (Text in French). [Wayback Machine link]
R. G. E. Pinch, Economical numbers, arXiv:math/9802046 [math.NT], 1998.
Eric Weisstein's World of Mathematics, Equidigital Number..
Wikipedia, Equidigital number.

Cf. A046759, A046760, A050252, A055642, A073048.

a046758 n = a046758_list !! (n-1)
a046758_list = filter (\n -> a050252 n == a055642 n) [1..]
-- Reinhard Zumkeller, Jun 21 2011

edQ[n_] := Total[IntegerLength[DeleteCases[Flatten[FactorInteger[n]], 1]]] == IntegerLength[n]; Join[{1}, Select[Range[140], edQ]] (* Jayanta Basu, Jun 28 2013 *)

for(n=1, 100, s=""; F=factor(n); for(i=1, #F[, 1], s=concat(s, Str(F[i, 1])); s=concat(s, Str(F[i, 2]))); c=0; for(j=1, #F[, 2], if(F[j, 2]==1, c++)); if(#digits(n)==#s-c, print1(n, ", "))) \\ Derek Orr, Jan 30 2015

from itertools import count, islice
from sympy import factorint
def A046758_gen(): # generator of terms
    return (n for n in count(1) if n == 1 or len(str(n)) == sum(len(str(p))+(len(str(e)) if e > 1 else 0) for p, e in factorint(n).items()))
A046758_list = list(islice(A046758_gen(),20)) # Chai Wah Wu, Feb 18 2022

A050252(a(n)) = A055642(a(n)). - Reinhard Zumkeller, Jun 21 2011

More terms from Eric W. Weisstein

A046760 Wasteful numbers.

Original entry on oeis.org

4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 108, 110, 114

Offset: 1

N. J. A. Sloane

Write n as product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n)>l(n).

A050252(a(n)) > A055642(a(n)). - Reinhard Zumkeller, Jun 21 2011

			For n = 125 = 5^3, l(n) = 3 but D(n) = 2. So 125 is not a term of this sequence. [clarified by _Derek Orr_, Jan 30 2015]

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
J.-P. Delahaye, Les chasseurs de nombres premiers.
R. G. E. Pinch, Economical numbers., arXiv:math/9802046 [math.NT], 1998.
Eric Weisstein's World of Mathematics, Wasteful Number.
Wikipedia, Extravagant number.

Cf. A046758, A046759.

a046760 n = a046760_list !! (n-1)
a046760_list = filter (\n -> a050252 n > a055642 n) [1..]
-- Reinhard Zumkeller, Aug 02 2013

Cases[Range[115], n_ /; Length[Flatten[IntegerDigits[FactorInteger[n] /. 1 -> Sequence[]]]] > Length[IntegerDigits[n]]] (* Jean-François Alcover, Mar 21 2011 *)

for(n=1,100,s="";F=factor(n);for(i=1,#F[,1],s=concat(s,Str(F[i,1]));s=concat(s,Str(F[i,2])));c=0;for(j=1,#F[,2],if(F[j,2]==1,c++));if(#digits(n)<#s-c,print1(n,", "))) \\ Derek Orr, Jan 30 2015

from itertools import count, islice
from sympy import factorint
def A046760_gen(): # generator of terms
    return (n for n in count(1) if len(str(n)) < sum(len(str(p))+(len(str(e)) if e > 1 else 0) for p, e in factorint(n).items()))
A046760_list = list(islice(A046760_gen(),20)) # Chai Wah Wu, Feb 18 2022

A254315 Number of distinct digits in the prime factorization of n (counting terms of the form p^1 as p).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 3, 3, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3

Offset: 2

Michel Lagneau, Jan 28 2015

Write n as product of primes raised to powers; then a(n) is the total number of distinct digits in product representation (number of distinct digits in all the primes and number of distinct digits in all the exponents that are greater than 1).
a(n)<=10. The least n such that a(n)=10 is n = 41701690 = 2*5*47*83*1069.
Property: a(p) = A043537(p), for p prime.
From Michel Marcus, Feb 21 2015: (Start)
For p in A038604, a(p^2) = A043537(p) + 1.
For p in A038611, a(p^3) = A043537(p) + 1.
For p in A038612, a(p^4) = A043537(p) + 1.
For p in A038613, a(p^5) = A043537(p) + 1.
For p in A038614, a(p^6) = A043537(p) + 1.
For p in A038615, a(p^7) = A043537(p) + 1.
For p in A038616, a(p^8) = A043537(p) + 1.
For p in A038617, a(p^9) = A043537(p) + 1.
(End)

			a(36)=2 because 36 = 2^2 * 3^2 => 2 distinct digits.
a(414)=2 because 414 = 2 * 3^2 * 23 => 2 distinct digits.

Michel Lagneau, Table of n, a(n) for n = 2..10000

Cf. A027748, A043537, A050252, A254317.

with(ListTools):
nn:=100:
  for n from 2 to nn do:
    n0:=length(n):lst:={}:x0:=ifactors(n):
    y:=Flatten(x0[2]):z:=convert(y,set):
    z1:=z minus {1}:nn0:=nops(z1):
     for k from 1 to nn0 do :
      t1:=convert(z1[k],base,10):z2:=convert(t1,set):
      lst:=lst union z2:
     od:
     nn1:=nops(lst):printf(`%d, `,nn1):
     od :

f[n_] := Block[{pf = FactorInteger@ n, i}, Length@ DeleteDuplicates@ Flatten@ IntegerDigits@ Rest@ Flatten@ Reap@ Do[If[Last[pf[[i]]] == 1, Sow@ First@ pf[[i]], Sow@ FromDigits@ Flatten[IntegerDigits /@ pf[[i]]]], {i, Length@ pf}]]; Array[f,100] (* Michael De Vlieger, Jan 29 2015 *)

print1(1,", ");for(k=2,100,s=[];F=factor(k);for(i=1,#F[,1],s=concat(s,digits(F[i,1]));if(F[i,2]>1,s=concat(s,digits(F[i,2]))));print1(#vecsort(s,,8),", ")) \\ Derek Orr, Jan 30 2015

from sympy import factorint
def A254315(n):
    return len(set([x for l in [[d for d in str(p)]+[d for d in str(e) if d != '1'] for p,e in factorint(n).items()] for x in l]))
# Chai Wah Wu, Feb 24 2015

A377369 a(n) = total number of bits in the binary representation of the prime factorization of n (including exponents > 1).

Original entry on oeis.org

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

Offset: 1

Paolo Xausa, Dec 27 2024

			a(10) = 5 because 10 = 2*5 = 10_2*101_2 (5 total bits).
a(18) = 6 because 18 = 2*3^2 = 10_2*11_2^10_2 (6 total bits).

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A050252 (analogous for base 10).

Cf. A070939.

A377369[n_] := Total[BitLength[Select[Flatten[FactorInteger[n]], # > 1 &]]];
Array[A377369, 100]

a(n)={my(f=factor(n)); sum(i=1, #f~, 1 + logint(f[i,1],2) + (f[i,2]>1) + logint(f[i,2],2))} \\ Andrew Howroyd, Dec 29 2024

from sympy import factorint
def a(n): return sum(len(bin(p)[2:])+(len(bin(e)[2:]) if e>1 else 0) for p, e in factorint(n).items())
print([a(n) for n in range(1, 91)]) # Michael S. Branicky, Dec 27 2024

A110475 Number of symbols '*' and '^' to write the canonical prime factorization of n.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 1, 1, 2, 0, 2, 0, 1, 1, 1, 1, 3, 0, 1, 1, 2, 0, 2, 0, 2, 2, 1, 0, 2, 1, 2, 1, 2, 0, 2, 1, 2, 1, 1, 0, 3, 0, 1, 2, 1, 1, 2, 0, 2, 1, 2, 0, 3, 0, 1, 2, 2, 1, 2, 0, 2, 1, 1, 0, 3, 1, 1, 1, 2, 0, 3, 1, 2, 1, 1, 1, 2, 0, 2, 2, 3, 0, 2, 0, 2, 2

Offset: 1

Reinhard Zumkeller, Sep 08 2005

nonn

It is conjectured that 1,2,3,4,5,6,7,9,11 are the only positive integers which cannot be represented as the sum of two elements of indices n such that a(n) = 1. - Jonathan Vos Post, Sep 11 2005

a(n) = 2 iff n is a sphenic number (A007304) or n is a prime p times a prime power q^e with e > 1 and q not equal to p. a(n) = 3 iff n has exactly four distinct prime factors (A046386); or n is the product of two prime powers (p^e)*(q^f) with e > 1, f > 1 and p not equal to q; or n is a semiprime s times a prime power r^g with g > 1 and r relatively prime to s. For a(n) > 3, Reinhard Zumkeller's description is a simpler description than the above compound descriptions. - Jonathan Vos Post, Sep 11 2005

			a(208029250) = a(2*5^3*11^2*13*23^2) = 4 '*' + 3 '^' = 7.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime Factorization.

Cf. A050252, A001358, A025475, A000040, A238949.
Cf. A007304, A046386, A008578.
Cf. A001221, A056170, A118914, A077761, A085548.

a110475 1 = 0
a110475 n = length us - 1 + 2 * length vs where
            (us, vs) = span (== 1) $ a118914_row n
-- Reinhard Zumkeller, Mar 23 2014

A110475[n_] := 2*Length[#] - 1 - Count[#, 1] & [FactorInteger[n][[All, 2]]];
Array[A110475, 100] (* Paolo Xausa, Mar 10 2025 *)

a(n) = A001221(n) - 1 + A056170(n) for n > 1.
a(n) = 0 iff n=1 or n is prime: a(A008578(n)) = 0.
a(n) = 1 iff n is a semiprime or a prime power p^e with e > 1.
From Amiram Eldar, Sep 27 2024: (Start)
a(n) = A238949(n) - 1 for n >= 2.
Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C - 1), where B is Mertens's constant (A077761) and C = Sum_{p prime} 1/p^2 (A085548). (End)

A192010 The smallest number with n digits in its prime factorization (total count of digits of all bases and exponents).

Original entry on oeis.org

1, 4, 12, 36, 132, 396, 1716, 5148, 25740, 87516, 437580, 1662804, 8314020, 38244492, 167943204, 839716020, 3862693692, 17298150012, 86490750060, 397857450276, 1850902051284, 9254510256420, 42570747179532, 201748323589956, 1008741617949780, 4640211442568988

Offset: 1

Reinhard Zumkeller, Jun 21 2011

A050252(a(n)) = n and A050252(m) <> n for m < a(n);

			a(2) = 4 = 2^2 and A050252(12) = (1+1) = 2;
a(3) = 12 = 2^2 * 3 and A050252(12) = (1+1) + 1 = 3;
a(4) = 36 = 2^2 * 3^2 and A050252(36) = (1+1) + (1+1) = 4;
a(5) = 132 = 2^2 * 3 * 11 and A050252(132) = (1+1) + 1 + 2 = 5;
a(6) = 396 = 2^2 * 3^2 * 11 and A050252(396) = (1+1) + (1+1) + 2 = 6;
a(7) = 1716 = 2^2 * 3 * 11 * 13 and A050252(1716) = (1+1) + 1 + 2 + 2 = 7;
a(8) = 5148 = 2^2 * 3^2 * 11 * 13 and A050252(5148) = (1+1) + (1+1) + 2 + 2 = 8;
a(9) = 25740 = 2^2 * 3^2 * 5 * 11 * 13 and A050252(25740) = (1+1) + (1+1) + 1 + 2 + 2 = 9;
a(10) = 87516 = 2^2 * 3^2 * 11 * 13 * 17 and A050252(87516) = (1+1) + (1+1) + 2 + 2 + 2 = 10;
a(11) = 437580 = 2^2 * 3^2 * 5 * 11 * 13 * 17 and A050252(437580) = (1+1) + (1+1) + 1 + 2 + 2 + 2 = 11;
a(12) = 1662804 = 2^2 * 3^2 * 11 * 13 * 17 * 19 and A050252(1662804) = (1+1) + (1+1) + 2 + 2 + 2 + 2 = 12;
a(13) = 8314020 = 2^2 * 3^2 * 5 * 11 * 13 * 17 * 19 and A050252(8314020) = (1+1) + (1+1) + 1 + 2 + 2 + 2 + 2 = 13.

import Data.List (elemIndex)
import Data.Maybe (fromJust)
a192010 n = succ $ fromJust $ elemIndex n $ map a050252 [1..]

a(14)-a(26) from Donovan Johnson, Jul 03 2011

cp's OEIS Frontend

A379373 Numbers k such that A050252(k) <= A055642(k).

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A055642 Number of digits in the decimal expansion of n.

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A046759 Economical numbers: write n as a product of primes raised to powers, let D(n) = number of digits in product, l(n) = number of digits in n; sequence gives n such that D(n) < l(n).

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A046758 Equidigital numbers.

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A046760 Wasteful numbers.

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A254315 Number of distinct digits in the prime factorization of n (counting terms of the form p^1 as p).

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