A265727
Least primitive weird number, pwn, (A002975) which is divisible by the n-th prime (A000040).
Original entry on oeis.org
70, 70, 836, 4030, 17272, 836, 7912, 7192, 4030, 113072, 83312, 7912, 8812312, 5830, 4199030, 9272, 91388, 10792, 23941578736, 786208, 682592, 569494624, 555616, 539744, 15126992, 73616, 519712
Offset: 3
a(6) is 4030 since it is the first pwn to be divisible by the sixth prime number, 13. 4030 = 13 * 310.
- 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.
Cf.
A002975,
A258250,
A258333,
A258374,
A258375,
A258401,
A258882,
A258883,
A258884,
A258885,
A265726,
A265728.
-
(* copy the terms from A002975, assign them equal to 'lst' and then *) f[n_] := Select[lst, Mod[#, Prime@ n] == 0 &][[1]]; Array[f, 27, 3]
A265726
Primitive weird numbers whose abundance is a record.
Original entry on oeis.org
70, 836, 7192, 9272, 73616, 243892, 338572, 1188256, 1901728, 3963968, 28279232, 36228736, 91322752, 141659096, 263144192, 351295232, 664373504, 2113834496, 5522263024, 6933503488, 19179527168, 22755515392, 31574500724, 98620009472, 135895635968
Offset: 1
a(1) = 70 since it is the first term in A002975; its abundance is 4.
a(2) is 836 since its abundance, 8, exceeds that of a(1); 4.
a(3) is 7192 = A002975(5) since its abundance, 16, exceeds that of a(2) and that of A002975(1..4).
Cf.
A002975,
A258250,
A258333,
A258374,
A258375,
A258401,
A258882,
A258883,
A258884,
A258885,
A265727,
A265728.
-
(* copy the terms from A002975, assign them equal to 'lst' and then *) f[n_] := DivisorSigma[1, n] - 2n; k = 1; lsu = {}; mx = 0; While[k < 647, ds = f@ lst[[k]]; If[ds > mx, mx = ds; AppendTo[lsu, lst[[k]]]]; k++]; lsu
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