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.

A280013 Numbers k such that sum of squarefree divisors of k > sum of squarefree divisors of m for all m < k.

Original entry on oeis.org

1, 2, 3, 5, 6, 10, 14, 21, 22, 26, 30, 42, 66, 78, 102, 114, 130, 138, 170, 174, 186, 210, 318, 330, 390, 462, 510, 546, 570, 690, 798, 858, 870, 930, 1110, 1218, 1230, 1290, 1410, 1554, 1590, 1722, 1770, 1830, 1974, 2010, 2130, 2190, 2310, 2730, 3390, 3570, 3990, 4290, 4830, 5610
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 14 2017

Keywords

Comments

Numbers k such that psi(rad(k)) > psi(rad(m)) for all m < k, where psi() is the Dedekind psi function (A001615) and rad() is the squarefree kernel (A007947).
Numbers k such that Sum_{d|k} mu(d)^2*d > Sum_{d|m} mu(d)^2*d for all m < k, where mu() is the Moebius function (A008683).
All terms are squarefree. - Robert Israel, Apr 19 2017

Links

Crossrefs

Cf. A001615, A002093, A002182, A007947, A008683, A034090, A048250, A174572.

Programs

  • Maple
    ssd:= n -> convert(select(numtheory:-issqrfree,numtheory:-divisors(n)),`+`):
M:= 0: A:= NULL:
for n from 1 to 10^5 do
    r:= ssd(n);
    if r > M then M:= r; A:= A, n fi
od:
A; # Robert Israel, Apr 19 2017
  • Mathematica
    mx = 0; t = {}; Do[u = DivisorSum[n, # &, SquareFreeQ[#] &]; If[u > mx, mx = u; AppendTo[t, n]], {n, 6000}]; t
  • Python
    from sympy.ntheory.factor_ import core
from sympy import divisors
def s(n): return sum(list(filter(lambda i: core(i) == i, divisors(n))))
def ok(n):
    m=1
    while ms(m): return False
        m+=1
    return True # Indranil Ghosh, Apr 16 2017

A281782 Numbers n such that sum of prime power divisors of n > sum of prime power divisors of m for all m < n.

Original entry on oeis.org

2, 3, 4, 7, 8, 16, 27, 32, 64, 121, 125, 128, 243, 256, 512, 729, 1024, 2048, 4096, 6561, 8192, 15625, 16384, 32761, 32768, 59049, 65536, 117649, 130321, 131072, 177147, 262144, 524287, 524288, 1048576, 1594323, 1953125, 2097152, 4194304, 8388608
Offset: 1

Views

Author

Ilya Gutkovskiy, Apr 14 2017

Keywords

Comments

Numbers n such that A023889(n) > A023889(m) for all m < n.
Numbers n such that Sum_{p^k|n, p prime, k>=1} p^k > Sum_{p^k|m, p prime, k>=1} p^k for all m < n.

Links

Crossrefs

Cf. A002093, A002182, A023889, A034090, A174572, A246655, A280013.

Programs

  • Mathematica
    mx = 0; t = {}; Do[u = DivisorSum[n, # &, PrimePowerQ[#] &]; If[u > mx, mx = u; AppendTo[t, n]], {n, 8500000}]; t

A290514 Numbers n such that product of odd divisors of n > product of odd divisors of m for all m < n.

Original entry on oeis.org

1, 3, 5, 7, 9, 15, 21, 27, 33, 35, 39, 45, 63, 75, 99, 105, 135, 165, 189, 195, 225, 315, 495, 525, 585, 675, 693, 735, 765, 819, 825, 855, 945, 1155, 1365, 1485, 1575, 2205, 2475, 2835, 3465, 4095, 4725, 5355, 5775, 5985, 6435, 6615, 6825, 7245, 7425, 7875, 8085, 8415, 8505, 8775, 8925, 9009, 9135, 9405
Offset: 1

Views

Author

Ilya Gutkovskiy, Aug 04 2017

Keywords

Comments

Numbers n such that A136655(n) > A136655(m) for all m < n.

Crossrefs

Cf. A034287, A034288, A136655, A174572, A182469.

Programs

  • Mathematica
    mx = 0; t = {}; Do[u = Product[d, {d, Select[Divisors[n], OddQ[#] &]}]; If[u > mx, mx = u; AppendTo[t, n]], {n, 9500}]; t
Showing 1-3 of 3 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.