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.

A348930 a(n) = A038502(sigma(n)), where A038502 is fully multiplicative with a(3) = 1, and a(p) = p for any other prime p.

Original entry on oeis.org

1, 1, 4, 7, 2, 4, 8, 5, 13, 2, 4, 28, 14, 8, 8, 31, 2, 13, 20, 14, 32, 4, 8, 20, 31, 14, 40, 56, 10, 8, 32, 7, 16, 2, 16, 91, 38, 20, 56, 10, 14, 32, 44, 28, 26, 8, 16, 124, 19, 31, 8, 98, 2, 40, 8, 40, 80, 10, 20, 56, 62, 32, 104, 127, 28, 16, 68, 14, 32, 16, 8, 65, 74, 38, 124, 140, 32, 56, 80, 62, 121, 14, 28
Offset: 1

Views

Author

Antti Karttunen, Nov 04 2021

Keywords

Comments

Note that a(A005820(4)) = A005820(4) and a(A005820(6)) = A005820(6), i.e., the fourth and sixth 3-perfect numbers, 459818240 and 51001180160 are among the fixed points of this sequence, precisely because they are also terms of A323653. As the former factorizes as 459818240 = 256 * 5 * 7 * 19 * 37 * 73, it must follow that a(256)/256 * a(5)/5 * a(7)/7 * a(19)/19 * a(37)/37 * a(73)/73 = 1, because ratio a(n)/n is multiplicative. See also comments in A348738.

Links

Crossrefs

Cf. A000203, A000265, A005820, A038502, A323653, A348738, A348931, A348932.
Cf. also A161942, A336457.

Programs

  • Mathematica
    s[n_] := n / 3^IntegerExponent[n, 3]; Table[s[DivisorSigma[1, n]], {n, 1, 100}] (* Amiram Eldar, Nov 04 2021 *)
  • PARI
    A038502(n) = (n/3^valuation(n, 3));
A348930(n) = A038502(sigma(n));

Formula

Multiplicative with a(p^e) = A038502(1 + p + p^2 + ... + p^e).
a(n) = A038502(A000203(n)).
For all n >= 1, A000265(a(n)) = A336457(n).

A336458 Numbers k for which A065330(k) = A065330(sigma(k)).

Original entry on oeis.org

1, 2, 3, 6, 28, 40, 84, 120, 135, 224, 270, 496, 672, 819, 1488, 1638, 3780, 8128, 10880, 24384, 30240, 32640, 32760, 66960, 167400, 174592, 406224, 523776, 1097280, 2178540, 3138345, 6276690, 6517665, 6656832, 8910720, 10480640, 13035330, 14705145, 17428320, 23569920, 29410290, 31441920, 33550336
Offset: 1

Views

Author

Antti Karttunen, Jul 24 2020

Keywords

Comments

Numbers k for which A065330(k) = A336457(k).
Question: Is this a subsequence of A336461?

Links

Crossrefs

Cf. A000203, A065330, A336457.
Cf. A336461.
Subsequences: A000396, A005820.

Programs

A336459 a(n) = A065330(sigma(sigma(n))), where A065330 is fully multiplicative with a(2) = a(3) = 1, and a(p) = p for primes p > 3.

Original entry on oeis.org

1, 1, 7, 1, 1, 7, 5, 1, 7, 13, 7, 7, 1, 5, 5, 1, 13, 7, 7, 1, 7, 91, 5, 7, 1, 1, 5, 5, 1, 65, 7, 13, 31, 5, 31, 7, 5, 7, 5, 13, 1, 7, 7, 7, 7, 65, 31, 7, 5, 1, 65, 19, 5, 5, 65, 5, 31, 13, 7, 5, 1, 7, 35, 1, 7, 403, 7, 13, 7, 403, 65, 7, 19, 5, 7, 7, 7, 5, 31, 1, 133, 13, 7, 7, 35, 7, 5, 91, 13, 91, 31, 5, 85, 403
Offset: 1

Views

Author

Antti Karttunen, Jul 25 2020

Keywords

Comments

Sequence removes prime factors 2 and 3 from the prime factorization A051027(n) = sigma(sigma(n)).
Like A051027, neither this is multiplicative. For example, we have a(3) = 7, a(7) = 5, but a(21) = 7 <> 35. However, for example, a(10) = 13, and a(3*10) = a(3)*a(10) = 65.

Links

Crossrefs

Cf. A000203, A051027, A065330, A336456 (similar sequence), A336457.
Cf. also A336561 (positions where this appears to be multiplicative but A051027 does not).

Programs

Formula

a(n) = A336457(A000203(n)) = A065330(A051027(n)).
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.