A091340 Amicable numbers with property that each member m of the corresponding amicable pair is divisible by sopfr(m) (the sum of prime factors with repetition, A001414).

821921625, 988676775, 4024942087978, 4179223134422, 100733767393275, 110452715806725

Offset

1,1

Comments

Both members of the amicable pair appear in the sequence.

Conjecture: sequence is finite (even though there are many known amicable numbers - about 8*10^7 currently).

Sergei Chernykh and the teams @Boinc found a new pair with their still ongoing search in the 21-digit range, 109297847965212832096 with sopfr(m)=118618 and 109392896505354817184 with sopfr(m)=39152. - Sven Simon, Sep 19 2020

Links

Table of n, a(n) for n=1..6.

Sergei Chernykh, Amicable pairs list

J. O. M. Pedersen, Tables of Aliquot Cycles [Broken link]

J. O. M. Pedersen, Tables of Aliquot Cycles [Via Internet Archive Wayback-Machine]

J. O. M. Pedersen, Tables of Aliquot Cycles [Cached copy, pdf file only]

Example

a(1): 821921625 = 3^2*5^3*7*29*59*61, sopfr(n) = 177 = 3*59.
a(2): 988676775 = 3^2*5^2*71*199*311, sopfr(n) = 597 = 3*199.

Crossrefs

Cf. A001414, A046346, A063990, A259180 (amicable pairs).

Cf. A267076 (amicable pairs that have the same sopfr).

Sequence in context: A152156 A017540 A132216 * A114665 A229800 A182239

Adjacent sequences: A091337 A091338 A091339 * A091341 A091342 A091343

Keyword

nonn,more

Author

Sven Simon, Dec 31 2003

Status

approved