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.

A386422 Odd numbers k that are closer to being perfect than previous terms and also satisfy the condition that A324644(k)/A324198(k) = 2.

Original entry on oeis.org

3, 33, 99, 135, 855, 2295, 19575, 38745, 63855, 121485, 371925, 3870195, 8109585, 28306005, 36340395, 113215095, 463084245, 672363615, 675916395, 686574735, 1208140395
Offset: 1

Views

Author

Antti Karttunen, Jul 21 2025

Keywords

Comments

Questions: Are there only multiples of 5 after the three initial terms? Are there any common terms with A228058?

Crossrefs

Apart from initial 3, a subsequence of A364286.
Cf. also A171929, A228059, A386419, A386420, A386421 for similar sequences.

Programs

  • PARI
    A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
    is_A364286(n) = if(isprime(n), 0, my(u=A276086(n)); (gcd(sigma(n),u)==2*gcd(n,u))); \\ Antti Karttunen, Jul 21 2025
    m=-1; n=-1; k=0; while(m!=0, n+=2; if(!((n-1)%(2^25)),print1("("n")")); if(isprime(n) || is_A364286(n), if((m<0) || abs((sigma(n)/n)-2)
    				

A386419 Odd numbers k that are closer to being perfect than previous terms, and also satisfy the condition that phi(k) = phi(sigma(k)).

Original entry on oeis.org

1, 3, 15, 45, 585, 2295, 11475, 29835, 72675, 424575, 7977165, 28851975, 29277885, 39317175
Offset: 1

Views

Author

Antti Karttunen, Jul 21 2025

Keywords

Comments

Questions: Is 45 the only term also in A228058? (See also A354362). Are there only multiples of 5 after the two initial terms?
If it exists, a(15) > 2^30 (1073741824).

Crossrefs

Programs

  • PARI
    A353680(n) = ((n%2) && (eulerphi(sigma(n))==eulerphi(n)));
    isA353679(n) = A353680(n);
    m=-1; n=0; k=0; while(m!=0, n++; if(!(n%(2^25)),print1("("n")")); if(isA353679(n), if((m<0) || abs((sigma(n)/n)-2)
    				

A386420 Odd numbers k that are closer to being perfect than previous terms and also satisfy the conditions that sigma(k) preserves the 3-adic valuation of k, and that sigma(k) == -k (mod 3).

Original entry on oeis.org

7, 15, 105, 495, 1365, 2205, 9405, 26145, 31815, 497835, 654675, 1984455, 7188885, 9018009, 9338595, 9958905, 13777785, 13800465, 14571585, 47020995, 78867495, 132884115, 210124665, 363860775
Offset: 1

Views

Author

Antti Karttunen, Jul 21 2025

Keywords

Comments

Question: Is 2205 the only term also in A228058?
If it exists, a(25) > 1275068416.

Crossrefs

Subsequence of A349752, thus also of A349749 and of A349751.
Cf. A000203.

Programs

  • PARI
    isA349752(n) = if(!(n%2), 0, my(s=sigma(n)); (0==(s+n)%3) && valuation(s, 3)==valuation(n, 3));
    m=-1; n=0; k=0; while(m!=0, n++; if(!(n%(2^25)),print1("("n")")); if(isA349752(n), if((m<0) || abs((sigma(n)/n)-2)
    				
Showing 1-3 of 3 results.