A388846 The smallest start of a run of exactly n consecutive positive integers for which the number of exponential divisors of their factorials is strictly decreasing.

1, 7, 20, 79, 131, 1040, 960, 1386, 11451, 58924, 112559, 169458, 767186, 287358, 8914348, 1700634, 8164372, 176195964, 71280725, 150479502

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Mathematica

d[n_] := d[n] = DivisorSigma[0, n]; d[0] = 1;
r[n_] := Product[d[(n - DigitSum[n, p])/(p - 1)] / d[(n - 1 - DigitSum[n - 1, p])/(p - 1)], {p, FactorInteger[n][[;; , 1]]}]; r[1] = 1;
seq[len_] := Module[{v = Table[0, {len}], nsuc = 0, c = 0, k = 1, m}, While[c < len, m = nsuc; If[r[k] < 1, nsuc++, If[k > m && m <= len && v[[m]] == 0, v[[m]] = k - m; c++]; nsuc = 1]; k++]; v]; seq[12]

Prog

(PARI) d(n) = if(n == 0, 1, numdiv(n));
r(n) = {my(p = factor(n)[, 1]); prod(i = 1, #p, d((n - sumdigits(n, p[i]))/(p[i] - 1)) / d((n - 1 - sumdigits(n - 1, p[i]))/(p[i] - 1))); }
list(len) = {my(v = vector(len), nsuc = 0, c = 0, k = 1, m); while(c < len, m = nsuc; if(r(k) < 1, nsuc++, if(k > m && m > 0 && m <= len && v[m] == 0, v[m] = k-m; c++); nsuc = 1); k++); v; }

Crossrefs

Cf. A000142, A049419, A322791, A388840, A388842, A388844, A388845.

Sequence in context: A301777 A299181 A299944 * A265657 A298214 A299346

Adjacent sequences: A388843 A388844 A388845 * A388847 A388848 A388849

Keyword

nonn,more

Author

Amiram Eldar, Sep 21 2025

Status

approved