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.

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).

Links

Crossrefs

Subsequence of A353679.
Cf. A000010, A000203, A000396, A228058, A354362.
Cf. also A171929, A228059, A386420, A386421, A386422.

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.

Links

Crossrefs

Subsequence of A349752, thus also of A349749 and of A349751.
Cf. A000203.
Cf. also A171929, A228059, A386419, A386421, A386422.

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)

A386421 Odd numbers k that are closer to being perfect than previous terms and also satisfy the condition that gcd(k, A003961(k)) is equal to gcd(sigma(k), A003961(k)), where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors function.

Original entry on oeis.org

1, 3, 9, 21, 63, 135, 855, 1485, 25245, 34155, 43785, 46035, 1665825, 1805475, 22982505, 125011845, 127371195, 657814575
Offset: 1

Views

Author

Antti Karttunen, Jul 21 2025

Keywords

Comments

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

Links

Crossrefs

Subsequence of A349174.
Cf. A000203, A000396, A003961.
Cf. also A171929, A228059, A386419, A386420, A386422 for similar sequences.

Programs

  • PARI
    A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
is_A349174(n) = if(!(n%2), 0, my(u=A003961(n)); gcd(u, sigma(n))==gcd(u, n));
m=-1; n=-1; k=0; while(m!=0, n+=2; if(!((n-1)%(2^25)),print1("("n")")); if(is_A349174(n), if((m<0) || abs((sigma(n)/n)-2)

A387165 Nondeficient numbers k for which A324644(k)/A324198(k) = 2.

Original entry on oeis.org

38745, 77805, 78435, 118755, 141075, 157815, 210735, 237195, 241605, 294975, 300105, 323505, 364455, 371925, 390195, 409185, 455715, 475335, 499905, 567945, 607635, 660825, 701415, 733005, 766395, 806085, 809325, 872235, 885465, 891135, 937755, 964845, 978705, 1101555, 1150065, 1201095, 1229445, 1265355, 1293705
Offset: 1

Views

Author

Antti Karttunen, Aug 28 2025

Keywords

Comments

First three nonmultiples of 5 occur at a(138), a(276), a(356) = 4446981, 8909901, 11234223. (Cf. A005231, A064001).

Links

Crossrefs

Intersection of A023196 and A364286.
Cf. A000203, A276086.
Cf. also A371082, A386422, A387163 and A047802, A064001, A115414.

Programs

  • PARI
    A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
is_A387165(n) = if(sigma(n)<2*n, 0, my(u=A276086(n)); (gcd(sigma(n),u)==2*gcd(n,u)));

Formula

{k | sigma(k) >= 2*k, A324644(k) = 2*A324198(k)}.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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