A364294 -id:A364294 - cp's OEIS frontend

A364258 a(n) = A163511(n) - n.

1, 1, 2, 0, 4, 4, 0, -2, 8, 18, 8, 14, 0, 2, -4, -8, 16, 64, 36, 106, 16, 54, 28, 26, 0, 20, 4, 8, -8, -8, -16, -20, 32, 210, 128, 590, 72, 338, 212, 304, 32, 184, 108, 202, 56, 102, 52, 74, 0, 86, 40, 124, 8, 52, 16, 22, -16, 6, -16, -4, -32, -28, -40, -50, 64, 664, 420, 3058, 256, 1806, 1180, 2330, 144, 1052, 676

Offset: 0

Antti Karttunen, Jul 25 2023

Compare also to the scatter plot of A364294.

Antti Karttunen, Table of n, a(n) for n = 0..12288

Cf. A007283, A163511, A364255 [= gcd(n,a(n))], A364287 (positions of negative terms), A364292 (of terms <= 0), A364288, A364294 [= -a(A364293(n))].

f[n_] := Reverse@ Map[Ceiling[(Length@ # - 1)/2] &, DeleteCases[Split@ Join[Riffle[IntegerDigits[n, 2], 0], {0}], {k__} /; k == 1]]; {1}~Join~Table[-n + Function[t, Prime[t] Product[Prime[m]^(f[n][[m]]), {m, t}] ][DigitCount[n, 2, 1]], {n, 120}] (* Michael De Vlieger, Jul 25 2023 *)

from sympy import nextprime
def A364258(n):
    c, p, k = 1, 1, n
    while k:
        c *= (p:=nextprime(p))**(s:=(~k&k-1).bit_length())
        k >>= s+1
    return c*p-n # Chai Wah Wu, Jul 25 2023

a(n) = A364288(A163511(n)).
For n >= 1, a(2*n) = 2*a(n).
For n >= 0, a(A007283(n)) = 0.

A364293 Odd numbers k for which A163511(k) <= k.

Original entry on oeis.org

3, 7, 15, 29, 31, 59, 61, 63, 119, 121, 123, 125, 127, 223, 239, 245, 247, 249, 251, 253, 255, 383, 447, 479, 493, 495, 497, 499, 501, 503, 505, 507, 509, 511, 767, 895, 957, 959, 989, 991, 999, 1001, 1003, 1005, 1007, 1009, 1011, 1013, 1015, 1017, 1019, 1021, 1023, 1535, 1789, 1791, 1917, 1919, 1977, 1979, 1981

Offset: 1

Antti Karttunen, Jul 25 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 1..15157; terms less than 2^23

Odd terms in A364292.

Cf. A000225 (subsequence apart from its two initial terms), A163511, A364294 [= -A364258(a(n))].

A364563 Difference k - A005940(k) computed for those odd numbers k for which the difference is nonnegative.

Original entry on oeis.org

0, 0, 0, 2, 6, 20, 2, 48, 28, 4, 110, 80, 48, 18, 18, 234, 202, 166, 110, 132, 12, 64, 42, 24, 484, 446, 402, 348, 360, 238, 50, 68, 276, 132, 246, 186, 204, 240, 994, 940, 884, 824, 830, 690, 462, 526, 722, 560, 240, 192, 680, 300, 596, 194, 602, 614, 696, 2012, 1958, 1898, 1794, 1840, 1624, 1336, 1442, 1724, 1458

Offset: 1

Antti Karttunen, Aug 06 2023

Antti Karttunen, Table of n, a(n) for n = 1..11023

Cf. A005940, A364499, A364543.

Cf. also A364294.

a(n) = -A364499(A364543(n)).

cp's OEIS Frontend

A364258 a(n) = A163511(n) - n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

Formula

A364293 Odd numbers k for which A163511(k) <= k.

Views

Author

Keywords

Links

Crossrefs

A364563 Difference k - A005940(k) computed for those odd numbers k for which the difference is nonnegative.

Views

Author

Keywords

Links

Crossrefs

Formula