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 1-5 of 5 results.

A255425 a(n) = A003557(A255334(n)) = A255334(n) / A255424(n).

Original entry on oeis.org

36, 36, 36, 36, 36, 36, 36, 180, 36, 576, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 396, 900, 36, 36, 36, 36, 36, 36, 576, 36, 36, 36, 36, 36, 36, 468, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 576, 36, 36
Offset: 1

Views

Author

Antti Karttunen, Apr 06 2015

Keywords

Links

Crossrefs

Cf. A003557, A254791, A255334, A255424, A255426.

Formula

a(n) = A003557(A255334(n)) = A255334(n) / A255424(n).
For all n, a(n) > 1 and a(n) < A255426(n).

A255426 a(n) = A003557(A255423(n)) = A255423(n) / A255424(n).

Original entry on oeis.org

49, 49, 49, 49, 49, 49, 49, 245, 49, 676, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 539, 1225, 49, 49, 49, 49, 49, 49, 676, 49, 49, 49, 49, 49, 49, 637, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 676, 49, 49
Offset: 1

Views

Author

Antti Karttunen, Apr 06 2015

Keywords

Links

Crossrefs

Cf. A003557, A254791, A255423, A255424, A255425.

Formula

a(n) = A003557(A255423(n)) = A255423(n) / A255424(n).
For all n, a(n) > A255425(n) > 1.

A255334 Numbers n for which there exists k > n such that A000203(k) = A000203(n) and A007947(k) = A007947(n), where A000203 gives the sum of divisors, and A007947 gives the squarefree kernel of n.

Original entry on oeis.org

1512, 7560, 16632, 19656, 25704, 28728, 34776, 37800, 43848, 44928, 46872, 55944, 61992, 65016, 71064, 80136, 83160, 89208, 92232, 98280, 101304, 107352, 110376, 119448, 125496, 128520, 134568, 143640, 146664, 152712, 155736, 161784, 164808, 170856, 173880, 182952, 189000, 192024, 198072, 207144, 210168, 216216
Offset: 1

Views

Author

Antti Karttunen, Mar 23 2015

Keywords

Comments

None of the terms are squarefree, because if there were such x, then we would have rad(x) = x, and for any value k > x such that rad(k) = x we would have k = y*x, for some strictly positive integer y, and in that case sigma(k) > sigma(x). Thus all terms are members of sequence A013929.
None of the terms in range a(1) .. a(6589) occur in A255335. Are the sequences disjoint forever?

Links

Crossrefs

Subsequence of A013929.
Cf. A000203, A007947.
Cf. also A255423 (gives the corresponding k), A255335 (same sequence sorted into ascending order, with duplicates removed), A255412 [gives sigma(a(n))], A255424 [gives rad(a(n))], A255425, A254035, A254791.

Programs

  • PARI
    A007947(n) = factorback(factorint(n)[, 1]); \\ Andrew Lelechenko, May 09 2014
isA255334(n) = { my(r=A007947(n), s=sigma(n), k=n+r); while(kA007947(k) == r), return(1), k = k+r)); return(0); };
i=0; for(n=1, 2^25, if(isA255334(n), i++; write("b255334.txt", i, " ", n)))
  • Scheme
    ;; With Antti Karttunen's IntSeq-library. Quite naive and slow implementation.
(define A255334 (MATCHING-POS 1 1 isA255334?))
(define (isA255334? n) (let ((sig_n (A000203 n)) (rad_n (A007947 n))) (let loop ((try (+ n rad_n))) (cond ((>= try sig_n) #f) ((and (= sig_n (A000203 try)) (= rad_n (A007947 try))) #t) (else (loop (+ try rad_n)))))))

Formula

a(n) = A255424(n) * A255425(n).

A255423 The least number k > A255334(n) for which A000203(k) = A000203(A255334(n)) and A007947(k) = A007947(A255334(n)), where A000203 gives the sum of divisors, and A007947 gives the squarefree kernel of n.

Original entry on oeis.org

2058, 10290, 22638, 26754, 34986, 39102, 47334, 51450, 59682, 52728, 63798, 76146, 84378, 88494, 96726, 109074, 113190, 121422, 125538, 133770, 137886, 146118, 150234, 162582, 170814, 174930, 183162, 195510, 199626, 207858, 211974, 220206, 224322, 232554, 236670, 249018, 257250, 261366, 269598, 281946, 286062, 294294
Offset: 1

Views

Author

Antti Karttunen, Apr 06 2015

Keywords

Links

Crossrefs

Cf. A000203, A007947, A255334.
Cf. also A255335 (same sequence sorted into ascending order), A255424 (squarefree kernel of a(n)), A255426 (same terms with but with their squarefree kernel divided out of them).

Programs

  • PARI
    A007947(n) = factorback(factorint(n)[, 1]);
nextone(n) = { if(!n,return(0)); my(r=A007947(n), s=sigma(n), k=n+r); while(kA007947(k) == r), return(k), k = k+r)); return(0); };
i=0; for(n=1, 2^25, k = nextone(n); if(k, i++; write("b255423.txt", i, " ", k))); \\ Andrew Lelechenko, May 09 2014

Formula

a(n) = A255424(n) * A255426(n).

A255412 a(n) = A000203(A255334(n)).

Original entry on oeis.org

4800, 28800, 57600, 67200, 86400, 96000, 115200, 148800, 144000, 142800, 153600, 182400, 201600, 211200, 230400, 259200, 345600, 288000, 297600, 403200, 326400, 345600, 355200, 384000, 403200, 518400, 432000, 576000, 470400, 489600, 499200, 518400, 528000, 547200, 691200, 638400, 748800, 614400, 633600, 662400, 672000, 806400, 864000, 856800, 720000
Offset: 1

Views

Author

Antti Karttunen, Apr 05 2015

Keywords

Comments

Sequence gives value of sigma(n) for numbers n for which there exists k > n such that A000203(k) = A000203(n) and A007947(k) = A007947(n), where A000203 gives the sum of divisors, and A007947 gives the squarefree kernel of n. The sequence is ordered by the magnitude of n, and contains duplicates, because there are cases of multiple such pairs having the same value of sigma.
The first such duplicate values occur as a(17) = a(22) = 345600 and a(20) = a(25) = 403200.

Links

Crossrefs

Cf. A254035 (same sequence sorted into ascending order, with duplicates removed).
Cf. A000203, A007947, A255334, A255423, A255424.

Programs

Formula

a(n) = A000203(A255334(n)).
a(n) = A000203(A255423(n)).
Showing 1-5 of 5 results.

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