cp's OEIS Frontend

A372300 Numbers k such that k and k+1 are both primitive infinitary abundant numbers (definition 1, A372298).

%I A372300 #5 Apr 27 2024 03:36:19
%S A372300 812889,3181815,20787584,181480695,183872535,307510664,337206344,
%T A372300 350158808,523403264,744074624,868421504,1063361144,1955365125,
%U A372300 2076191864,2578966215,3672231255,4185590408,5032685384,7158001304,8348108535,10784978295,16264812135,20917209495,24514454055
%N A372300 Numbers k such that k and k+1 are both primitive infinitary abundant numbers (definition 1, A372298).
%C A372300 The corresponding sequence with definition 2 (A372299) coincides with this sequence for the first 24 terms.
%o A372300 (PARI) isidiv(d, f) = {my(bne,bde); if (d==1, return (1)); for (k=1, #f~, bne = binary(f[k, 2]); bde = binary(valuation(d, f[k, 1])); if (#bde < #bne, bde = concat(vector(#bne-#bde), bde)); for (j=1, #bne, if (! bne[j] && bde[j], return (0)); ); ); return (1); }
%o A372300 idivs(n) = {my(f = factor(n), d = divisors(f), idiv = []); for (k=1, #d, if (isidiv(d[k], f), idiv = concat(idiv, d[k])); ); idiv; } \\ _Michel Marcus_ at A077609
%o A372300 isigma(n) = {my(f = factor(n), b); prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], 1+f[i, 1]^(2^(#b-k)), 1)))} ;
%o A372300 isab(n) = isigma(n) > 2*n;
%o A372300 isprim(n) = select(x -> x<n && isigma(x) >= 2*x, idivs(n)) == [];
%o A372300 lista(kmax) = {my(is1 = 0, is2); for(k = 2, kmax, is2 = isab(k); if(is1 && is2, if(isprim(k-1) && isprim(k), print1(k-1, ", "))); is1 = is2);}
%Y A372300 Subsequence of A129656, A327635 and A372298.
%Y A372300 Cf. A372299.
%Y A372300 Similar sequences: A283418, A330872, A361935.
%K A372300 nonn
%O A372300 1,1
%A A372300 _Amiram Eldar_, Apr 25 2024