A054903 -id:A054903 - cp's OEIS frontend

A015914 Numbers k such that sigma(k) + 6 = sigma(k+6).

5, 7, 11, 13, 17, 23, 31, 37, 41, 47, 53, 61, 67, 73, 83, 97, 101, 103, 104, 107, 131, 147, 151, 157, 167, 173, 191, 193, 223, 227, 233, 251, 257, 263, 271, 277, 307, 311, 331, 347, 353, 367, 373, 383, 433, 443, 457, 461, 503, 541, 557, 563, 571

Offset: 1

Robert G. Wilson v

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A000203.

See A054903 for nonprimes. - Reinhard Zumkeller, Jan 27 2009

Select[Range[50000], DivisorSigma[1, #] + 6==DivisorSigma[1, # + 6] &] (* Vincenzo Librandi, Mar 10 2014 *)

A054904 x = a(n) is the smallest composite number such that sigma(x+6n) = sigma(x)+6n, where sigma = A000203.

Original entry on oeis.org

104, 65, 20, 80, 44, 125, 45, 63, 40, 99, 56, 70, 296, 125, 88, 110, 104, 145, 212, 182, 80, 170, 333, 105, 369, 185, 184, 135, 180, 301, 356, 185, 1859, 329, 176, 195, 4916, 434, 612, 287, 140, 185, 776, 255, 524, 413, 344, 205, 272, 329, 567, 215, 320, 469

Offset: 1

Labos Elemer, May 23 2000

nonn

If sigma(x+d) = sigma(x)+d and d = 6k, then composite solutions seem to be more frequent and arise sooner.

a(725) > 3*10^11 (if it exists). - Donovan Johnson, Sep 23 2013

			n = 20, 6n = 120, a(20) = 182, sigma(182)+120 = 336+120 = 456 = sigma(182+120) = sigma(302).

Donovan Johnson, Table of n, a(n) for n = 1..724

Cf. A015914-A015917, A023200-A023203, A054799, A054903-A054905.

Table[x = 4; While[Nand[CompositeQ@ x, DivisorSigma[1, x + 6 n] == DivisorSigma[1, x] + 6 n], x++]; x, {n, 54}] (* Michael De Vlieger, Feb 18 2017 *)

/* finds first 696 terms */ mx=7695851; s=vector(mx); for(j=4, mx, if(isprime(j)==0, s[j]=sigma(j))); for(n=1, 696, n6=n*6; for(x=4, 7691753, if(s[x]>0, if(s[x+n6]==s[x]+n6, write("b054904.txt", n " " x); next(2))))) /* Donovan Johnson, Sep 23 2013 */

sigma(x+6n) = sigma(x)+6n, a(n) = min(x) and it is composite.

A084293 a(n) = 2n + A054905(n).

Original entry on oeis.org

436, 305635361, 110, 35, 195566, 77, 26, 55, 38, 76, 938, 104, 212308, 85, 74, 106677, 86, 161

Offset: 1

Labos Elemer, May 26 2003

The sequence begins 436, 305635361, 110, 35, 195566, 77, 26, 55, 38, 76, 938, 104, 212308, 85, 74, 106677, 86, 161, ?, 91, 87, 92, 122, 111, 1585396, 145, 94, 76627, 10283, 159, 772, 133, 122, 412, 194, 142, 964, 205, 374, 925, 6725, 209, ?, 1015, 178, ?, ?, 206, 146, ?, ..., where the other missing terms (designated by "?") are unknown, if they exist (see also A206768).

			To terms of A054905, where sigma(x+2n)=sigma(x)+2n replacing x+2n=y,x=y-2n, we get sigma(y)-2n=sigma(y-2n);
For several analogous sequences, the corresponding "mirror-solutions" can be easily constructed. See: e.g. A015913-A015918; A050507, A054799, A054903-A054906; A054982-A054987; A059118; A055009, A055458, A063500, etc.

Cf. A054905.

Composite x satisfying sigma(x-2n) = sigma(x) - 2n.

A084292 a(n) = 6n + A054904(n).

Original entry on oeis.org

110, 77, 38, 104, 74, 161, 87, 111, 94, 159, 122, 142, 374, 209, 178, 206, 206, 253, 326, 302, 206, 302, 471, 249, 519, 341, 346, 303, 354, 481, 542, 377, 2057, 533, 386, 411, 5138, 662, 846, 527, 386, 437, 1034, 519, 794, 689, 626, 493, 566, 629, 873, 527, 638

Offset: 1

Labos Elemer, May 26 2003

nonn

Composite solutions y to sigma(y-6n) = sigma(y) - 6n. For terms x of A054904, where sigma(x+6n) = sigma(x) + 6n, replacing x+6n = y, x = y-6n, we get sigma(y) - 6n = sigma(y-6n).

Amiram Eldar, Table of n, a(n) for n = 1..724

Cf. A000203 (sigma), A054904, A084293.

For several analogous sequences such corresponding "mirror-solutions" can be easily constructed. See, e.g., A015913-A015918, A050507, A054799, A054903-A054906, A054982-A054987, A059118, A055009, A055458, A063500, etc.

cp's OEIS Frontend

A015914 Numbers k such that sigma(k) + 6 = sigma(k+6).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A054904 x = a(n) is the smallest composite number such that sigma(x+6n) = sigma(x)+6n, where sigma = A000203.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A084293 a(n) = 2n + A054905(n).

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula

A084292 a(n) = 6n + A054904(n).

Views

Author

Keywords

Comments

Links

Crossrefs