A066750 -id:A066750 - cp's OEIS frontend

A306354 a(n) = gcd(n, A101337(n)).

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 3, 1, 1, 3, 1, 1, 9, 1, 1, 3, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 25, 1, 1, 1, 1, 5, 1, 1, 1, 1, 12, 1, 2, 9, 4, 1, 6, 1, 4, 3, 7, 1, 1, 1, 1, 1, 1, 7, 1, 1, 16, 1, 2, 1, 4, 1, 2, 1, 8, 1, 9

Offset: 1

Ctibor O. Zizka, Feb 09 2019

A101337(n) / n = r, r an integer, gives A306360. A101337(n) / n = 1 gives A005188. n / A101337(n) = s, s an integer, gives A306361. The motivation for this sequence was the question as to which numbers n have the property A101337(n) / n = r and the property n / A101337(n) = s?

			For n = 24, a(24) = gcd(24, 2*2 + 4*4) = gcd(24,20) = 4, thus a(24) = 4;
for n = 153, a(153) = gcd(153, 1*1*1 + 5*5*5 + 3*3*3) = gcd(153,153) = 153, thus a(153) = 153.

Cf. A005188, A066750, A101337.

Array[GCD[#1, Total[#2^Length[#2]]] & @@ {#, IntegerDigits@ #} &, 90] (* Michael De Vlieger, Feb 09 2019 *)

a(n) = my(d=digits(n)); gcd(n, sum(i=1, #d, d[i]^#d)); \\ Michel Marcus, Feb 12 2019

from math import gcd
def A306354(n): return gcd(n,sum(int(d)**len(str(n)) for d in str(n))) # Chai Wah Wu, Jan 26 2022

A081653 Greatest common divisor of sums of decimal digits of n and of n-th prime.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 4, 1, 1, 1, 2, 1, 2, 1, 1, 2, 5, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 7, 1, 1, 2, 11, 1, 1, 2, 1, 1, 2, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 16, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 5, 1

Offset: 1

Reinhard Zumkeller, Mar 25 2003

			a(8) = GCD(A007953(8), A007953(A000040(8))) = GCD(8, A007953(19)) = GCD(8,1+9) = GCD(4*2,5*2) = 2.

Cf. A000040, A007953, A007605, A081652, A066750.

A081653[n_Integer]:=GCD[Plus@@IntegerDigits[n],Plus@@IntegerDigits[Prime[n]]]; Table[A081653[n],{n,105}] (* Enrique Pérez Herrero, Aug 07 2010 *)

a(n) = GCD(A007953(n), A007605(n)).

A081652 Greatest common divisor of n and sum of decimal digits of n-th prime.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 7, 1, 8, 1, 1, 1, 4, 1, 2, 1, 1, 1, 2, 1, 4, 1, 5, 1, 1, 11, 1, 7, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 11, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 8, 1, 1, 1, 4, 1, 2, 1, 8, 1, 2, 1, 10, 1, 17, 1, 4

Offset: 1

Reinhard Zumkeller, Mar 25 2003

			a(16) = GCD(16, A007953(A000040(16))) = GCD(16, A007953(53)) = GCD(16,5+3) = GCD(8*2,8) = 8.

Cf. A000040, A007953, A081653, A066750.

Table[GCD[n,Total[IntegerDigits[Prime[n]]]],{n,110}] (* Harvey P. Dale, Jul 12 2012 *)

a(n) = GCD(n, A007605(n)).

A348192 a(0) = 0; for n >= 1, a(n) = 1 + a(n - GCD(n, digital sum(n))).

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 3, 4, 3, 4, 5, 2, 3, 3, 3, 4, 5, 3, 4, 4, 3, 5, 6, 4, 5, 6, 5, 6, 7, 4, 5, 6, 5, 5, 6, 5, 6, 6, 5, 7, 8, 5, 6, 6, 6, 7, 8, 6, 7, 8, 7, 8, 9, 7, 8, 8, 7, 9, 10, 8, 9, 9, 9, 8, 9, 8, 9, 10, 9, 10, 9, 10, 11, 9, 9, 10, 11, 9, 10, 10, 10, 10, 11, 10, 11, 12, 11, 12, 13, 12, 13

Offset: 0

Ctibor O. Zizka, Jan 25 2022

Number of steps needed to reach zero when starting from k = n and repeatedly applying the map that replaces k by k - A066750(k).

			n = 12, a(12) = 1 + a(12 - GCD(12,3)) = 1 + a(9) = 1 + 1 + a(9 - GCD(9,9)) = 2 + a(0) = 2.

Cf. A007953, A066750.

a[0] = 0; a[n_] := a[n] = 1 + a[n - GCD[n, Plus @@ IntegerDigits[n]]]; Array[a, 100, 0] (* Amiram Eldar, Jan 25 2022 *)

from itertools import count, islice
from math import gcd
def A348192_gen(): # generator of terms
    blist = [0]
    yield 0
    for n in count(1):
        blist.append(1+blist[n-gcd(n,sum(int(d) for d in str(n)))])
        yield blist[-1]
A348192_list = list(islice(A348192_gen(),30)) # Chai Wah Wu, Jan 26 2022

a(0) = 0; for n >= 1, a(n) = 1 + a(n - A066750(n)).

A365762 Greatest common divisor of n and the product of its digits.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 1, 2, 5, 2, 1, 2, 1, 20, 1, 2, 1, 8, 5, 2, 1, 4, 1, 30, 1, 2, 3, 2, 5, 18, 1, 2, 3, 40, 1, 2, 1, 4, 5, 2, 1, 16, 1, 50, 1, 2, 1, 2, 5, 2, 1, 2, 1, 60, 1, 2, 9, 8, 5, 6, 1, 4, 3, 70, 1, 2, 1, 2, 5, 2, 7, 2, 1, 80, 1, 2, 1, 4, 5, 2, 1, 8, 1, 90, 1, 2, 3, 2, 5, 6, 1, 2, 9, 100

Offset: 1

Simon R Blow, Sep 18 2023

This sequence will contain all numbers whose prime factors are exclusively <10 (7-smooth numbers, A002473).

			a(11)=1 as 1*1=1; 11 and 1 share 1 as a gcd.
a(15)=5 as 1*5=5; 15 and 5 share 5 as a gcd.
a(10)=10 as 1*0=0; 10 and 0 share 10 as a gcd.

Cf. A066750, A007954, A002473, A214587.

a[n_]:=GCD[n,Product[Part[IntegerDigits[n],i],{i,IntegerLength[n]}]]; Array[a,100] (* Stefano Spezia, Sep 20 2023 *)

a(n) = gcd(n, vecprod(digits(n))); \\ Michel Marcus, Sep 20 2023

from math import gcd, prod
def a(n): return gcd(n, prod(map(int, str(n))))
print([a(n) for n in range(1, 101)])

cp's OEIS Frontend

A306354 a(n) = gcd(n, A101337(n)).

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A081653 Greatest common divisor of sums of decimal digits of n and of n-th prime.

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A081652 Greatest common divisor of n and sum of decimal digits of n-th prime.

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Formula

A348192 a(0) = 0; for n >= 1, a(n) = 1 + a(n - GCD(n, digital sum(n))).

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Formula

A365762 Greatest common divisor of n and the product of its digits.

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Author

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Programs

Mathematica

PARI

Python