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).

Links

Crossrefs

Cf. A000203, A000720, A052382, A098686, A098683, A098684.

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

A098683 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.

Original entry on oeis.org

123, 5224, 11166, 51174, 172451, 546322, 14355351, 23539612, 23539621, 24322837, 122924349, 4575242147, 42256772524, 283186883151, 623286236455, 665318971119, 665318971191, 5257788212426, 27452719198281, 273643846355134, 787812731751347, 787812731751374
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 24 2004

Keywords

Comments

a(n) must necessarily be a zeroless number, i.e., the sequence is a subsequence of A052382. - Chai Wah Wu, Mar 04 2019

Examples

			122924349 is in the sequence because pi(122924349) = P(1)*P(2)*P(2)*P(9)*P(2)*P(4)*P(3)*P(4)*P(9) where P(i) is i-th prime.

Crossrefs

Cf. A052382, A097227, A098684, A098685, A160040.

Programs

  • Mathematica
    Do[d=IntegerDigits[n];k=Length[d];If[ !MemberQ[d, 0]&&PrimePi[n]==Product[Prime[d[[j]]], {j, k}], Print[n]], {n, 230000000}]

Extensions

Entries corrected by Robert G. Wilson v, May 04 2009
a(13)-a(17) from Donovan Johnson, Jul 12 2010
a(18) from Giovanni Resta, Apr 01 2017
a(19) from Chai Wah Wu, Mar 05 2019
a(20)-a(22) from Chai Wah Wu, Mar 06 2019

A098771 Numbers n such that sigma(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

1, 2, 3, 4, 5, 6, 7, 8, 9, 38, 58, 66, 87, 568, 766, 2799, 6478, 6785, 26486, 36685, 36893, 64788, 66758, 67586, 69664, 77686, 276895, 467683, 474668, 488973, 548678, 587667, 658648, 666369, 668954, 839666, 939669, 958968, 968765, 2386698
Offset: 1

Views

Author

Farideh Firoozbakht, Oct 03 2004

Keywords

Comments

Number of terms of this sequence up to 15000000 is 72. Has this sequence at least one multi-digit prime term?

Examples

			97888745 is in the sequence because sigma(97888745) = 117936000 = sigma(9)*sigma(7)*sigma(8)*sigma(8)*sigma(8)*sigma(7)*sigma(4)*sigma(5).

Crossrefs

Cf. A098684, A098685.

Programs

  • Mathematica
    Do[If[h=IntegerDigits[n];l=Length[h];!MemberQ[h, 0]&&DivisorSigma[ 1, n]==Product[DivisorSigma[1, h[[k]]], {k, l}], Print[n]] {n, 100000000}]
Select[Range[24*10^5],DivisorSigma[1,#]==Times@@DivisorSigma[1, IntegerDigits[ #]]&] (* Harvey P. Dale, Mar 07 2018 *)

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

Cf. A110071, A110072, A097220, A097223, A097227, A098683, A098684, A098685.
Showing 1-4 of 4 results.

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