A307187 Numbers k such that A095112(k)/k sets a new record.

1, 2, 4, 6, 8, 12, 24, 48, 60, 120, 240, 360, 720, 1440, 1680, 2520, 5040, 10080, 15120, 20160, 30240, 50400, 55440, 110880, 166320, 221760, 332640, 665280, 1108800, 1330560, 1441440, 1663200, 2882880, 3326400, 4324320, 7207200, 8648640, 14414400, 17297280

Offset

1,2

Comments

k is in the sequence iff k is in position k in row k of A307081; in other words, iff A307088(k) = k.

Links

Table of n, a(n) for n=1..39.

Example

With f(k) = A095112(k)/k,
f(1) = 0, new record, so 1 is in the sequence;
f(2) = 1/2, new record, so 2 is in the sequence;
f(3) = 1/3;
f(4) = 1/2 + 1/4 = 3/4, new record, so 4 is in the sequence;
f(5) = 1/5;
f(6) = 1/2 + 1/3 = 5/6, new record, so 6 is in the sequence;
etc.

Prog

(PARI)
f(n)={my(s=0, T); T=factorint(n); for(i=1, #T[, 1], for(j=1, T[i, 2], s+=1/T[i, 1]^j)); s}
prog(n)={my(V, v, j); V=List(); for(k=1, n, v=f(k)+0.; j=setsearch(V, v, 1); if(j==k, print1(k, ", ")); if(j==0, print("err"); return, listinsert(V, v, j)))}

Crossrefs

Cf. A095112, A307081, A307088.

Sequence in context: A301414 A333953 A333963 * A340014 A001217 A131885

Adjacent sequences: A307184 A307185 A307186 * A307188 A307189 A307190

Keyword

nonn

Author

Luc Rousseau, Mar 28 2019

Status

approved