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));

A387712 Primitive terms of A387711: numbers k for which A003959(k) > 2*k, but for all whose proper divisors d|k, dA003959(d) <= 2*d.

Original entry on oeis.org

4, 18, 27, 30, 42, 45, 50, 63, 66, 70, 78, 102, 114, 138, 174, 186, 222, 246, 258, 282, 318, 354, 366, 375, 402, 426, 438, 474, 498, 525, 534, 582, 606, 618, 625, 642, 654, 678, 686, 735, 762, 786, 822, 825, 834, 894, 906, 942, 975, 978, 1002, 1038, 1074, 1078, 1086, 1089, 1146, 1158, 1182, 1194, 1210, 1266, 1274, 1275
Offset: 1

Views

Author

Antti Karttunen, Sep 06 2025

Keywords

Links

Crossrefs

Cf. A003959, A387711, A387713.
Positions of 1's in A387715.
Cf. also A091191, A337372.

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.

A387723 Numbers k for which A107758(k) > 2*k, and also for some of the proper divisors d|k, dA107758(d) > 2*d.

Original entry on oeis.org

12, 18, 20, 24, 28, 30, 36, 40, 42, 44, 45, 48, 50, 52, 54, 56, 60, 66, 68, 70, 72, 75, 76, 78, 80, 84, 88, 90, 92, 96, 98, 100, 102, 104, 105, 108, 110, 112, 114, 116, 120, 124, 126, 130, 132, 135, 136, 138, 140, 144, 148, 150, 152, 154, 156, 160, 162, 164, 165, 168, 170, 172, 174, 176, 180, 182, 184, 186, 188
Offset: 1

Views

Author

Antti Karttunen, Sep 06 2025

Keywords

Comments

Not the same as positions of terms > 1 in A387725. For example, A387725(225) = 3, although 225 is not present in this sequence.

Links

Crossrefs

Cf. A107758, A387725.
Setwise difference A387721 \ A387722.
Cf. also A341610, A387713.

Programs

  • PARI
    A107758(n) =  { my(f = factor(n)); prod(k=1, #f~, 1+sigma(f[k, 1]^f[k, 2])); };
is_A387723(n) = if((A107758(n)<=(2*n)), 0, fordiv(n, d, if(dA107758(d)>(2*d), return(1))); (0));
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.