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

812889, 3181815, 20787584, 181480695, 183872535, 307510664, 337206344, 350158808, 523403264, 744074624, 868421504, 1063361144, 1955365125, 2076191864, 2578966215, 3672231255, 4185590408, 5032685384, 7158001304, 8348108535, 10784978295, 16264812135, 20917209495, 24514454055

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<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

Adjacent sequences: A372297 A372298 A372299 * A372301 A372302 A372303

Keyword

nonn

Author

Amiram Eldar, Apr 25 2024

Status

approved