A325802 Numbers with one more divisor than distinct subset-sums of their prime indices.

12, 30, 40, 63, 70, 112, 154, 165, 198, 220, 273, 286, 325, 351, 352, 364, 442, 525, 550, 561, 595, 646, 675, 714, 741, 748, 765, 832, 850, 874, 918, 931, 952, 988, 1045, 1173, 1254, 1334, 1425, 1495, 1539, 1564, 1653, 1666, 1672, 1771, 1794, 1798, 1870, 1900

Offset

1,1

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. A subset-sum of an integer partition is any sum of a submultiset of it.

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of the partitions counted by A325835.

Links

Table of n, a(n) for n=1..50.

Formula

A000005(a(n)) = 1 + A299701(a(n)).

Example

The sequence of terms together with their prime indices begins:
   12: {1,1,2}
   30: {1,2,3}
   40: {1,1,1,3}
   63: {2,2,4}
   70: {1,3,4}
  112: {1,1,1,1,4}
  154: {1,4,5}
  165: {2,3,5}
  198: {1,2,2,5}
  220: {1,1,3,5}
  273: {2,4,6}
  286: {1,5,6}
  325: {3,3,6}
  351: {2,2,2,6}
  352: {1,1,1,1,1,5}
  364: {1,1,4,6}
  442: {1,6,7}
  525: {2,3,3,4}
  550: {1,3,3,5}
  561: {2,5,7}

Mathematica

Select[Range[100], DivisorSigma[0, #]==1+Length[Union[hwt/@Divisors[#]]]&]

Crossrefs

Positions of 1's in A325801.

Cf. A000005, A056239, A108917, A112798, A276024, A299701, A299702.

Cf. A325694, A325780, A325781, A325799, A325800, A325835.

Sequence in context: A145469 A024364 A093507 * A326019 A334804 A328411

Adjacent sequences: A325799 A325800 A325801 * A325803 A325804 A325805

Keyword

nonn

Author

Gus Wiseman, May 23 2019

Status

approved