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 A372300 Numbers k such that k and k+1 are both primitive infinitary abundant numbers (definition 1, A372298). 1
 812889, 3181815, 20787584, 181480695, 183872535, 307510664, 337206344, 350158808, 523403264, 744074624, 868421504, 1063361144, 1955365125, 2076191864, 2578966215, 3672231255, 4185590408, 5032685384, 7158001304, 8348108535, 10784978295, 16264812135, 20917209495, 24514454055 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding sequence with definition 2 (A372299) coincides with this sequence for the first 24 terms. LINKS Table of n, a(n) for n=1..24. PROG (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); } 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 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)))} ; isab(n) = isigma(n) > 2*n; isprim(n) = select(x -> x= 2*x, idivs(n)) == []; 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); } CROSSREFS Subsequence of A129656, A327635 and A372298. Cf. A372299. Similar sequences: A283418, A330872, A361935. Sequence in context: A344239 A344240 A238522 * A210060 A237790 A247058 Adjacent sequences: A372297 A372298 A372299 * A372301 A372302 A372303 KEYWORD nonn AUTHOR Amiram Eldar, Apr 25 2024 STATUS approved

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Last modified July 18 04:54 EDT 2024. Contains 374377 sequences. (Running on oeis4.)