cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A098685 Numbers n such that pi(n) = sigma(d_1)*sigma(d_2)*...*sigma(d_k) where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

15, 155, 252, 916, 1189, 12654, 55293, 177554, 418634, 753248, 885193, 18252678, 18252687, 18469156, 18469165, 19882616, 19882623, 41867246, 73526936, 73526957, 233843449, 244895519, 2345784285, 2399877831, 4273447776, 29891923496, 42649454852, 728781494646
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 24 2004

Keywords

Comments

a(n) must necessarily be a zeroless number. - Chai Wah Wu, Mar 04 2019

Examples

			885193 is in the sequence because pi(885193) = sigma(8)*sigma(8)*sigma(5)*sigma(1)*sigma(9)*sigma(3).
		

Crossrefs

Programs

  • Mathematica
    Do[d=IntegerDigits[n];k=Length[d];If[ !MemberQ[d, 0]&&PrimePi[n]== Product[DivisorSigma[1, d[[j]]], {j, k}], Print[n]], {n, 10000000}]

Extensions

a(12)-a(25) from Donovan Johnson, Jun 18 2009
a(26)-a(28) from Chai Wah Wu, Mar 04 2019

A098684 Numbers n such that pi(n) = P(d_1!!)*P(d_2!!)*...*P(d_k!!) where d_1 d_2 ... d_k is the decimal expansion of n and P(i) is i-th prime.

Original entry on oeis.org

10, 30, 123, 41402, 1400523, 3173000, 3173001, 3173010, 3173011, 351226103, 351226113, 351226130, 351226131
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 24 2004

Keywords

Comments

There are no further terms up to 35000000.
From Farideh Firoozbakht, Jun 01 2009: (Start)
If 10*n is in the sequence and 10*n+1 is composite then 10*n+1 is also in the sequence.
There is no further term up to 1.5*10^10. (End)
There are no other terms less than 10^15. - Chai Wah Wu, Mar 06 2019

Examples

			3173011 is in the sequence because pi(3173011)=P(3!!)*P(1!!)*P(7!!)*P(0!!)*P(1!!)*P(1!!).
		

Crossrefs

Programs

  • Mathematica
    Do[d=IntegerDigits[n];k=Length[d];If[PrimePi[n]== Product[Prime[d[[j]]!! ], {j, k}], Print[n]], {n, 35000000}]

Extensions

More terms from Farideh Firoozbakht, Jun 01 2009

A110070 Numbers n such that n=pi(d_1!*d_2!*...*d_k!) where d_1 d_2 ... d_k is the decimal expansion of n.

Original entry on oeis.org

0, 3, 34, 52, 2800414
Offset: 1

Views

Author

Farideh Firoozbakht, Jul 22 2005

Keywords

Comments

No other terms below 10^15. - Max Alekseyev, Jul 21 2024

Examples

			2800414 is in the sequence because 2800414=pi(2!*8!*0!*0!*4!*1!*4!).
		

Crossrefs

A160040 Numbers n such that pi(n) = prime(d_1)*prime(d_2)* ... *prime(d_k), where d_1, d_2, ... d_k is the decimal expansion of n, and the zeroth prime is 1.

Original entry on oeis.org

123, 2407, 5224, 8350, 11166, 30843, 51174, 66026, 172451, 202774, 266109, 546322, 1082682, 1830188, 1882036, 2754207, 3351809, 14355351, 23539612, 23539621, 24322837, 63950931, 122924349, 161485470, 204868903, 204868930, 252704792
Offset: 1

Views

Author

Robert G. Wilson v, Apr 30 2009

Keywords

Comments

See the references in A008578 for a discussion concerning the zeroth prime.

Crossrefs

Cf. A008578, A113581. A098683 is a proper subset.

Programs

  • Mathematica
    c = 0; k = 1; lst = {}; fQ[n_] := ( c == Times @@ (IntegerDigits@ n /. {0 -> 1, 1 -> 2, 2 -> 3, 3 -> 5, 4 -> 7, 5 -> 11, 6 -> 13, 7 -> 17, 8 -> 19, 9 -> 23}) ); While[k < 6000000000, If[PrimeQ@k, c++, If[ fQ@k, AppendTo[lst, k]; Print@k]]; k++ ]; lst
Showing 1-4 of 4 results.