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.

A387711 Numbers k for which A003959(k) > 2*k, where A003959 is multiplicative with a(p^e) = (p+1)^e.

Original entry on oeis.org

4, 8, 12, 16, 18, 20, 24, 27, 28, 30, 32, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 63, 64, 66, 68, 70, 72, 76, 78, 80, 81, 84, 88, 90, 92, 96, 100, 102, 104, 108, 112, 114, 116, 120, 124, 126, 128, 132, 135, 136, 138, 140, 144, 148, 150, 152, 156, 160, 162, 164, 168, 172, 174, 176, 180, 184, 186, 188, 189, 192, 196
Offset: 1

Views

Author

Antti Karttunen, Sep 06 2025

Keywords

Links

Crossrefs

Cf. A003959, A387710.
Disjoint union of A387712 and A387713. Positions of nonzero terms in A387715.
Subsequence of A005101, and of A246282.
After the initial 4 also a subsequence of A033942.

Programs

  • PARI
    A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
is_A387711(n) = (A003959(n)>(2*n));

A387713 Nonprimitive terms of A387711: numbers k for which A387715(k) > 1.

Original entry on oeis.org

8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 54, 56, 60, 64, 68, 72, 76, 80, 81, 84, 88, 90, 92, 96, 100, 104, 108, 112, 116, 120, 124, 126, 128, 132, 135, 136, 140, 144, 148, 150, 152, 156, 160, 162, 164, 168, 172, 176, 180, 184, 188, 189, 192, 196, 198, 200, 204, 208, 210, 212, 216, 220, 224, 225, 228, 232, 234
Offset: 1

Views

Author

Antti Karttunen, Sep 06 2025

Keywords

Links

Crossrefs

Cf. A003959.
Setwise difference A387711 \ A387712. Positions of terms > 1 in A387715.
Subsequence of A341610.

Programs

Formula

{k | A387715(k) > 1}.

A387715 Number of divisors d of n for which A003959(d) > 2*d, where A003959 is multiplicative with a(p^e) = (p+1)^e.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 3, 0, 1, 0, 2, 0, 0, 0, 4, 0, 0, 1, 2, 0, 1, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 1, 0, 2, 1, 0, 0, 6, 0, 1, 0, 2, 0, 3, 0, 4, 0, 0, 0, 5, 0, 0, 1, 5, 0, 1, 0, 2, 0, 1, 0, 7, 0, 0, 0, 2, 0, 1, 0, 6, 2, 0, 0, 5, 0, 0, 0, 4, 0, 4, 0, 2, 0, 0, 0, 8, 0, 0, 0, 4, 0, 1, 0, 4, 0
Offset: 1

Views

Author

Antti Karttunen, Sep 06 2025

Keywords

Comments

Number of terms of A387711 that divide n.

Links

Crossrefs

Cf. A003959, A387711 (positions of terms > 0), A387712 (of 1's), A387713 (of terms > 1).
Cf. also A080224, A337345.

Programs

Formula

a(n) = Sum_{d|n} [A003959(d) > 2*d], where [ ] is the Iverson bracket.

A387722 Numbers k for which A107758(k) > 2*k, but for all whose proper divisors d|k, dA107758(d) <= 2*d.

Original entry on oeis.org

6, 10, 14, 15, 21, 22, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94, 106, 118, 122, 134, 142, 146, 158, 166, 178, 194, 202, 206, 214, 218, 226, 254, 262, 274, 278, 298, 302, 314, 326, 334, 346, 358, 362, 382, 385, 386, 394, 398, 422, 429, 446, 454, 455, 458, 466, 478, 482, 502, 514, 526, 538, 542, 554, 561, 562, 566
Offset: 1

Views

Author

Antti Karttunen, Sep 06 2025

Keywords

Comments

Not the same as the positions of 1's in A387725.

Links

Crossrefs

Cf. A107758, A387725.
Setwise difference A387721 \ A387723.
Cf. also A091191, A337372, A387712.

Programs

  • PARI
    A107758(n) =  { my(f = factor(n)); prod(k=1, #f~, 1+sigma(f[k, 1]^f[k, 2])); };
is_A387722(n) = if((A107758(n)<=(2*n)), 0, fordiv(n, d, if(dA107758(d)>(2*d), return(0))); (1));
Showing 1-4 of 4 results.

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