A063680 Solutions to sigma(k) + 7 = sigma(k+7).

74, 531434, 387420482, 2541865828322

Offset: 1

Author

Jud McCranie, Jul 28 2001

Keywords

• nonn
• bref
• hard
• more

Comments

No other solutions < 4290000000. Sequence A063679 shows how to generate more solutions, but there may be solutions other than those produced by A063679.

No others < 10^17. - Seth A. Troisi, Oct 25 2022

k or k+7 must be a square or twice a square (A028982). See comment in A015886. - Seth A. Troisi, Oct 26 2022

From Jon E. Schoenfield, Oct 26 2022: (Start)

Each of the first 4 terms of the sequence is of the form k = 9^j - 7:

74 = 9^2 - 7,

531434 = 9^6 - 7,

387420482 = 9^9 - 7,

2541865828322 = 9^13 - 7.

The next terms of this form are 9^53 - 7 and 9^82 - 7.

Does the sequence contain any terms that are not of this form?

(End)

No other terms < 2.7*10^15. - Jud McCranie, Jul 27 2025

Examples

			sigma(74) + 7 = 121 = sigma(74+7), so 74 is in the sequence.
		

Crossrefs

Cf. A000203, A063679.

Cf. A054799, A015913, A015914, A015915, A015916, A015917, A054905.

Programs

PARI

isok(k) = sigma(k) + 7 == sigma(k+7); \\ Michel Marcus, Oct 25 2022

Extensions

a(4) from Seth A. Troisi, Oct 24 2022