A104483 -id:A104483 - cp's OEIS frontend

A104564 Number of distinct prime divisors of 77...771 (with n 7's).

1, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 1, 3, 4, 2, 2, 3, 2, 1, 4, 3, 1, 3, 3, 2, 3, 4, 2, 7, 1, 5, 6, 3, 3, 4, 3, 4, 5, 5, 3, 5, 4, 2, 3, 3, 6, 2, 2, 6, 5, 4, 3, 4, 4, 6, 2, 6, 5, 4, 4, 4, 5, 3, 3, 5, 2, 6, 3, 5, 5, 4, 6, 4, 6, 5, 3, 3, 4, 4, 4, 4, 6, 4, 3, 6, 5, 3

Offset: 1

Parthasarathy Nambi, Apr 20 2005

Also number of distinct prime factors of (10^(n + 1) - 1)*7/9 - 6. - Stefan Steinerberger, Mar 01 2006

			The number of distinct prime divisors of 71 is 1 (prime).
The number of distinct prime divisors of 771 is 2.
The number of distinct prime divisors of 7771 is 2.

Amiram Eldar, Table of n, a(n) for n = 1..231

Cf. A001221, A104484, A104483, A173806.

Cf. A104484 (3 instead of 7), A104659 (4 instead of 7), A104517 (5 instead of 7), A104890 (6 instead of 7), A105972 (8 instead of 7), A105259 (9 instead of 7).

Table[Length[FactorInteger[(10^(n + 1) - 1)*7/9 - 6]], {n, 1, 50}] (* Stefan Steinerberger, Mar 01 2006 *)
PrimeNu/@(FromDigits/@Table[PadLeft[{1},n,7],{n,2,55}])  (* Harvey P. Dale, Apr 22 2011 *)

a(n) = A001221(A173806(n+1)). - Amiram Eldar, Jan 24 2020

More terms from Stefan Steinerberger, Mar 01 2006

Offset corrected and more terms added by Amiram Eldar, Jan 24 2020

A104524 Number of distinct prime divisors of 55...557 (with n 5s).

Original entry on oeis.org

2, 1, 1, 2, 1, 3, 3, 3, 1, 3, 2, 5, 3, 1, 4, 3, 3, 3, 4, 2, 1, 2, 7, 4, 4, 4, 4, 5, 4, 4, 3, 2, 3, 5, 3, 4, 3, 7, 2, 4, 2, 4, 4, 8, 2, 4, 3, 6, 3, 2, 4, 7, 7, 7, 5, 5, 6, 7, 2, 4, 6, 3, 5, 5, 2, 5, 2, 4, 5, 5, 3, 9, 10, 6, 5, 6, 4, 4, 4, 5, 4, 5, 3, 6, 6, 4, 1

Offset: 1

Parthasarathy Nambi, Apr 20 2005

			The number of distinct prime divisors of 57 is 2.
The number of distinct prime divisors of 557 is 1 (prime).
The number of distinct prime divisors of 5557 is 1 (prime).

Amiram Eldar, Table of n, a(n) for n = 1..192

Cf. A104484, A104483, A104518.

Cf. A001221, A178769.

A104524 := proc(n) local x ;x := [7,seq(5,k=1..n)] ; add(op(i,x)*10^(i-1),i=1..nops(x)) ; numtheory[factorset](%) ; nops(%) ; end proc: # R. J. Mathar, Aug 24 2011

Table[PrimeNu[(50*10^n + 13)/9], {n, 1, 50}](* G. C. Greubel, May 07 2017 *)
Table[PrimeNu[FromDigits[PadLeft[{7},n,5]]],{n,2,90}] (* Harvey P. Dale, Dec 03 2021 *)

a(n) = omega((5*10^(n+1)+13)/9); \\ Michel Marcus, May 08 2017

a(n) = A001221(A178769(n+1)). - R. J. Mathar, Aug 24 2011

More terms from Michel Marcus, May 08 2017

More terms from Amiram Eldar, Jan 25 2020

A104543 Number of distinct prime divisors of 55...559 (with n 5s).

Original entry on oeis.org

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

Offset: 1

Parthasarathy Nambi, Apr 20 2005

			The number of distinct prime divisors of 59 is 1 (prime).
The number of distinct prime divisors of 559 is 2.
The number of distinct prime divisors of 5559 is 3.

Amiram Eldar, Table of n, a(n) for n = 1..202

Cf. A104484, A104483.

A104543 := proc(n) local x ;x := [9,seq(5,k=1..n)] ; add(op(i,x)*10^(i-1),i=1..nops(x)) ; numtheory[factorset](%) ; nops(%) ; end proc: # R. J. Mathar, Aug 24 2011

Table[PrimeNu[(50*10^n + 31)/9], {n,0,50}] (* G. C. Greubel, May 10 2017 *)
Table[PrimeNu[FromDigits[PadLeft[{9},n,5]]],{n,2,90}] (* Harvey P. Dale, Apr 22 2020 *)

a(n) = A001221((31+50*10^n)/9). - R. J. Mathar, Aug 24 2011

More terms from Amiram Eldar, Jan 25 2020

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A104564 Number of distinct prime divisors of 77...771 (with n 7's).

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A104524 Number of distinct prime divisors of 55...557 (with n 5s).

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A104543 Number of distinct prime divisors of 55...559 (with n 5s).

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