A265728 Least primitive weird number, pwn, (A002975) whose abundance is divisible by the n-th prime (A000040), or 0 if no such pwn exists.

70, 232374697216, 73616, 9272, 243892, 343876, 4128448, 519712, 1901728, 338572, 5568448, 6621632, 272240768, 4960448, 7470272, 1673087984, 146279296, 5440192, 91322752, 8134208, 35442304, 286717696, 54962343424, 110232704, 6460864, 2812606976, 44473216, 141659096, 33736064, 58668928, 9537494528, 37499776, 292335872, 795730688, 530110208, 18657360896, 16995175424, 664373504, 266311424, 23049995264, 15152370176, 17124699136, 64015565312, 52059008

Offset

1,1

Comments

No odd weird number exists below 10^21. The search is done on the volunteer computing project yoyo@home. - Wenjie Fang, Feb 23 2014

Links

Table of n, a(n) for n=1..44.

Douglas E. Iannucci, On primitive weird numbers of the form 2^k*p*q, arXiv:1504.02761 [math.NT], 2015.

Linked In, Number Theory, A very big weird number

Giuseppe Melfi, On the conditional infiniteness of primitive weird numbers, Journal of Number Theory, Vol. 147, Feb 2015, pp. 508-514.

Wikipedia, Weird number

Example

a(1) = 70 since it is the least pwn whose abundance, 4, is divisible by the first prime, 2.
a(2) = 0 since there is no known odd pwn and if there were, there is no reason why the abundance would be == 0 (mod 3).
a(3) = 73616 since it is the first pwn whose abundance, 80, is divisible by the third prime, 5.

Mathematica

(* copy the terms from A002975, assign them equal to 'lst' and then *) f[n_] := Select[lst, Mod[ DivisorSigma[1, #] - 2#, Prime@ n] == 0 &][[1]]; Array[f, 30]

Crossrefs

Cf. A002975, A258250, A258333, A258374, A258375, A258401, A258882, A258883, A258884, A258885, A265726, A265727.

Sequence in context: A172680 A121338 A172776 * A186073 A087043 A126648

Adjacent sequences: A265725 A265726 A265727 * A265729 A265730 A265731

Keyword

nonn

Author

Douglas E. Iannucci and Robert G. Wilson v, Dec 14 2015

Status

approved