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

Author

Bernard Schott, Sep 17 2022

Keywords

• nonn
• base
• fini

Comments

As A009993 is finite, this sequence is necessarily finite.

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

Examples

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

Crossrefs

Cf. A009993, A357171, A357172, A160218.

Similar sequences: A093036, A340548, A355595.

Programs

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 *)

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

Extensions

More terms from Amiram Eldar, Sep 17 2022