login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A074140 Sum of least integers of prime signatures over all partitions of n. 9
1, 2, 10, 50, 346, 3182, 38770, 609290, 11226106, 250148582, 7057182250, 216512001950, 7903965900226, 321552174623162, 13779150603234010, 644574260638821590, 33968684108427733426, 1994885097404292104942, 121496572792097514728530, 8114030083731371137603190 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Old name was: Sum of terms in n-th group in A036035.

a(n) is also the sum of terms in n-th row of A063008, A087443 or A227955.

LINKS

Peter Luschny and Alois P. Heinz, Table of n, a(n) for n = 0..350

Eric Weisstein's World of Mathematics, Prime Signature

Wikipedia, Partition (number theory)

Wikipedia, Prime signature

Index entries for sequences related to prime signature

EXAMPLE

a(6) = 64+96+144+216+240+360+900+840+1260+4620+30030 = 38770.

MAPLE

b:= proc(n, i, j) option remember;

      `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, j)+

      `if`(i>n, 0, ithprime(j)^i*b(n-i, i, j+1))))

    end:

a:= n-> b(n$2, 1):

seq(a(n), n=0..40);  # Alois P. Heinz, Aug 03 2013

MATHEMATICA

b[n_, i_, j_] := b[n, i, j] = If[n == 0, 1, If[i<1, 0, b[n, i-1, j]+If[i>n, 0, Prime[j]^i*b[n-i, i, j+1]]]]; a[n_] := b[n, n, 1]; Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Feb 25 2014, after Alois P. Heinz *)

PROG

(Sage)

def A074140(n):

    L = []

    P = primes_first_n(n)

    for p in Partitions(n):

        m = mul(P[i]^pi for i, pi in enumerate(p))

        L.append(m)

    return add(L)

[A074140(n) for n in (0..20)]  # Peter Luschny, Aug 02 2013

CROSSREFS

Cf. A036035, A063008, A074139, A074141, A025487, A087443, A227955, A332626.

Sequence in context: A020088 A205772 A306336 * A128449 A037514 A037717

Adjacent sequences:  A074137 A074138 A074139 * A074141 A074142 A074143

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Aug 28 2002

EXTENSIONS

More terms from Alford Arnold, Sep 10 2002

a(10)-a(12) from Thomas A. Rockwell (LlewkcoRAT(AT)aol.com), Sep 30 2004

a(12) corrected by Peter Luschny, Aug 03 2013

New name from Alois P. Heinz, Aug 03 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 10 00:32 EDT 2022. Contains 356026 sequences. (Running on oeis4.)