A363295
Numbers k such that k and k+20 are consecutive unitary weird numbers (A064114).
Original entry on oeis.org
34121990, 34428290, 34766810, 34936070, 38014970, 38152010, 39506090, 39844610, 41400170, 42044990, 42552770, 42584990, 43769810, 46276490, 46308710, 47155010, 47324270, 47461310, 49016870, 49153910, 49323170, 49661690, 49863170, 50540210, 51015770, 51354290, 53079110
Offset: 1
34121990 is a term since 34121990 = A064114(53235) and 34122010 = 34121990 + 20 = A064114(53236) are consecutive unitary weird numbers.
A364975
Admirable numbers (A111592) with a record gap to the next admirable number.
Original entry on oeis.org
12, 30, 42, 88, 120, 140, 186, 534, 678, 6774, 7962, 77118, 94108, 152826, 478194, 662154, 935564, 1128174, 2028198, 6934398, 7750146, 8330924, 9984738, 10030804, 22956114, 62062566, 151040622, 284791602, 732988732, 804394974, 1151476732, 9040886574, 31302713634
Offset: 1
The first 5 admirable numbers are 12, 20, 24, 30 and 40. The differences between these terms are 8, 4, 6 and 10. The record gaps, 8 and 10, occur after the terms 12 and 30, which are the first two terms of this sequence.
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admQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2];
seq[kmax_] := Module[{s = {}, m = 12, dm = 0}, Do[If[admQ[k], d = k - m; If[d > dm, dm = d; AppendTo[s, m]]; m = k], {k, m + 1, kmax}]; s]; seq[10^6]
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isadm(n) = {my(ab=sigma(n)-2*n); ab>0 && ab%2 == 0 && ab/2 < n && n%(ab/2) == 0; }
lista(kmax) = {my(m = 12, dm = 0); for(k = m+1, kmax, if(isadm(k), d = k - m; if(d > dm, dm = d; print1(m, ", ")); m = k));}
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