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 1-3 of 3 results.

A112719 Numbers m such that pi(m) = d_1^1 + d_2^2 + ... + d_k^k where d_1 d_2 ... d_k is the decimal expansion of m.

Original entry on oeis.org

0, 12, 160, 253, 382, 3664, 4683, 9285, 66290, 207735, 390481, 3748380, 7884391, 9136095, 11187665, 12690170, 15008945, 32067066, 34152082, 43470982, 311506482, 315458182, 317195680, 317583584, 789530607, 803190747, 818360167
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 17 2005

Keywords

Comments

This sequence is finite and the largest term is less than 10^73.

Examples

			43470982 is in the sequence because pi(43470982) = 4^1 + 3^2 + 4^3 + 7^4 + 0^5 + 9^6 + 8^7 + 2^8 = 2631327.
		

Crossrefs

Programs

  • Mathematica
    Do[d=IntegerDigits[n];k=Length[d];If[PrimePi[n]==Sum[d[[j]]^j, {j, k}], Print[n]], {n, 0, 170000000}]

Extensions

a(21)-a(27) from Donovan Johnson, Nov 09 2010

A112720 Numbers m such that phi(m) = 1^d_1 + 2^d_2 + ... + k^d_k where d_1 d_2 ... d_k is the decimal expansion of m.

Original entry on oeis.org

1, 2, 6883, 1132856, 11059812
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 17 2005

Keywords

Comments

There is no further term up to 7*10^7.
a(6) > 10^12. - Giovanni Resta, Apr 13 2017
This sequence is full because for k > 10 and 10^k <= m < 10^(k+1), phi(m) > 10^k/f(10^k) > Sum_{i=1..k+1} i^9 >= Sum_{i=1..k+1} i^d_i, where f(n) = exp(gamma)*log(log(n)) + 2.5/log(log(n)) is given in A057635. - Jinyuan Wang, Aug 02 2020

Examples

			phi(11059812) = 1^1 + 2^1 + 3^0 + 4^5 + 5^9 + 6^8 + 7^1 + 8^2 so 11059812 is in the sequence.
		

Crossrefs

Programs

  • Mathematica
    Do[d=IntegerDigits[n];k=Length[d];If[EulerPhi[n]==Sum[j^d[[j]], {j, k}], Print[n]], {n, 70000000}]

A112721 Numbers m such that phi(m) = d_1^1 + d_2^2 + ... + d_k^k where d_1 d_2 ... d_k is the decimal expansion of m.

Original entry on oeis.org

1, 44, 84, 5676, 32186, 35097, 128476, 527048, 700298, 12141094, 43874279, 58730238, 303387848, 2277279428
Offset: 1

Views

Author

Farideh Firoozbakht, Sep 17 2005

Keywords

Comments

a(15) > 6*10^10. - Donovan Johnson, Nov 09 2010
All terms of this sequence are less than 2 * 10^42. - Charles R Greathouse IV, May 11 2012
a(15) > 10^12. - Giovanni Resta, Apr 12 2017

Examples

			phi(12141094) = 1^1 + 2^2 + 1^3 + 4^4 + 1^5 + 0^6 + 9^7 + 4^8 = 4848768 so 12141094 is in the sequence.
		

Crossrefs

Programs

  • Mathematica
    Do[d=IntegerDigits[n];k=Length[d];If[EulerPhi[n]==Sum[d[[j]]^j, {j, k}], Print[n]], {n, 30000000}]

Extensions

a(11)-a(12) from Farideh Firoozbakht, Jan 04 2009
a(13)-a(14) from Donovan Johnson, Nov 09 2010
Showing 1-3 of 3 results.