

A265728


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


2



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
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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. 508514.
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



