A357173 Positions of records in A357171, i.e., integers whose number of divisors whose decimal digits are in strictly increasing order sets a new record.

1, 2, 4, 6, 12, 24, 36, 48, 72, 144, 336, 468, 504, 936, 1008, 1512, 2520, 3024, 5040, 6552, 7560, 13104, 19656, 39312, 78624, 98280, 196560, 393120, 668304, 1244880, 1670760, 1867320, 3341520, 3734640, 7469280, 22407840, 26142480, 31744440, 52284960, 63488880

Offset

1,2

Comments

As A009993 is finite, this sequence is necessarily finite.

Corresponding records are 1, 2, 3, 4, 6, 8, 9, 10, 11, ...

Links

Table of n, a(n) for n=1..40.

Example

a(6) = 24 is in the sequence because A357171(24) = 8 is larger than any earlier value in A357171.

Mathematica

s[n_] := DivisorSum[n, 1 &, Less @@ IntegerDigits[#] &]; seq = {}; sm = 0; Do[If[(sn = s[n]) > sm, sm = sn; AppendTo[seq, n]], {n, 1, 10^4}]; seq (* Amiram Eldar, Sep 17 2022 *)

Prog

(PARI) isok(d) = Set(d=digits(d)) == d; \\ A009993
f(n) = sumdiv(n, d, isok(d)); \\ A357171
lista(nn) = my(r=0, list = List()); for (k=1, nn, my(m=f(k)); if (m>r, listput(list, k); r = m); ); Vec(list); \\ Michel Marcus, Sep 18 2022

Crossrefs

Cf. A009993, A357171, A357172, A160218.

Similar sequences: A093036, A340548, A355595.

Sequence in context: A307122 A309015 A355579 * A349424 A134865 A140753

Adjacent sequences: A357170 A357171 A357172 * A357174 A357175 A357176

Keyword

nonn,base,fini

Author

Bernard Schott, Sep 17 2022

Extensions

More terms from Amiram Eldar, Sep 17 2022

Status

approved