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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
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<n && isigma(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
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.)